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Automatic Control, IEEE Transactions on

Issue 1 • Date Jan 1996

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Displaying Results 1 - 21 of 21
  • On the reduction of certain frequency-shaped linear quadratic dissipative design problems to an H formulation

    Page(s): 121 - 125
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (560 KB)  

    This paper concerns a concept of frequency-based quadratic dissipativity and its reduction to an equivalent H (or μ) condition. The paper is motivated by the observation that a strictly proper system cannot be strictly passive; hence, results on the synthesis of positive real systems using the Cayley transform directly cannot be applied in most physical situations View full abstract»

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  • Necessary and sufficient conditions for quadratic stability and stabilizability of uncertain linear time-varying systems

    Page(s): 125 - 128
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (364 KB)  

    In this paper we consider linear time-varying systems subject to norm bounded, one block, structured uncertainties. First, given an unforced system, we find necessary and sufficient conditions for quadratic stability; then, considered a controlled system, we provide necessary and sufficient conditions for quadratic stabilizability both for the state and the output feedback case View full abstract»

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  • Linear estimation in Krein spaces. I. Theory

    Page(s): 18 - 33
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    The authors develop a self-contained theory for linear estimation in Krein spaces. The derivation is based on simple concepts such as projections and matrix factorizations and leads to an interesting connection between Krein space projection and the recursive computation of the stationary points of certain second-order (or quadratic) forms. The authors use the innovations process to obtain a general recursive linear estimation algorithm. When specialized to a state-space structure, the algorithm yields a Krein space generalization of the celebrated Kalman filter with applications in several areas such as H -filtering and control, game problems, risk sensitive control, and adaptive filtering View full abstract»

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  • Linear estimation in Krein spaces. II. Applications

    Page(s): 34 - 49
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    We have shown that several interesting problems in H-filtering, quadratic game theory, and risk sensitive control and estimation follow as special cases of the Krein-space linear estimation theory developed in Part I. We show that all these problems can be cast into the problem of calculating the stationary point of certain second-order forms, and that by considering the appropriate state space models and error Gramians, we can use the Krein-space estimation theory to calculate the stationary points and study their properties. The approach discussed here allows for interesting generalizations, such as finite memory adaptive filtering with varying sliding patterns View full abstract»

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  • New methods to design an integral variable structure controller

    Page(s): 140 - 143
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (332 KB)  

    This paper presents two methods to design a single-input/single-output integral variable structure system. Once an overall transfer function is selected, two simple ways are presented to determine the required switching surface and the control function. The proposed methods not only avoid transforming the original plant into a companion form, but also enable the resulting control system to achieve the asymptotic tracking for a step reference signal and disturbance rejection for a bounded disturbance signal simultaneously. Two examples are given to illustrate the effectiveness of the proposed methods View full abstract»

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  • On a class of marginally stable positive-real systems

    Page(s): 152 - 155
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    A class of marginally stable positive real systems is defined which is less restrictive than the previously published definitions of strictly positive real systems. A minimal realization and state-space characterization of such systems are presented, and it is proven that controllers belonging to this class robustly stabilize positive real plants View full abstract»

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  • Optimal control of wear processes

    Page(s): 112 - 115
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    Models for wear of machine proposed by Rishel are considered. Optimal control problems for these wear processes are solved explicitly. The method of similarity solutions is used View full abstract»

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  • Stabilization of uncertain linear systems: an LFT approach

    Page(s): 50 - 65
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    This paper develops machinery for control of uncertain linear systems described in terms of linear fractional transformations (LFTs) on transform variables and uncertainty blocks with primary focus on stabilization and controller parameterization. This machinery directly generalizes familiar state-space techniques. The notation of Q-stability is defined as a natural type of robust stability, and output feedback stabilizability is characterized in terms of Q-stabilizability and Q-detectability which in turn are related to full information and full control problems. Computation is in terms of convex linear matrix inequalities (LMIs), the controllers have a separation structure, and the parameterization of all stabilizing controllers is characterized as an LFT on a stable, free parameter View full abstract»

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  • An algorithm for checking stability of symmetric interval matrices

    Page(s): 133 - 136
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    A branch-and-bound algorithm for checking Hurwitz and Schur stability of symmetric interval matrices is proposed. The algorithm in a finite number of steps either verifies stability or finds a symmetric matrix which is not stable. It can also be used for checking positive definiteness of asymmetric interval matrices View full abstract»

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  • Duality and linear programs for stability and performance analysis of queuing networks and scheduling policies

    Page(s): 4 - 17
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    We consider the problems of performance analysis and stability/instability determination of queuing networks and scheduling policies. We exhibit a strong duality relationship between the performance of a system and its stability analysis via mean drift. We obtain a variety of linear programs (LPs) to conduct such stability and performance analyses. A certain LP, called the performance LP, bounds the performance of all stationary nonidling scheduling policies. If it is bounded, then its dual, called the drift LP, has a feasible solution which is a copositive matrix. The quadratic form associated with this copositive matrix has a negative drift, showing that all stationary nonidling scheduling policies result in a geometrically converging exponential moment. These results carry over to fluid models, allowing the study of networks with nonexponential distributions. If a modification of the performance LP, called the monotone LP, is bounded, then the system is stable. Finally, there is a another modification of the performance LP, called the finite time LP. It provides transient bounds on the performance of the system from any initial condition View full abstract»

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  • Linear and nonlinear stabilizing continuous controllers of uncertain dynamical systems including state delay

    Page(s): 116 - 121
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    The problem of robust stabilization of a class of time-varying dynamical systems with disturbance, uncertain parameters, and a bounded time-varying state delay is considered. Two classes of stabilizing continuous controllers are proposed. The proposed controllers can guarantee the existence of the solution to the dynamical system in the usual sense and can also be directly implemented in the practical control problems. Moreover, since the proposed controllers are completely independent of the time delay (which is only assumed to be any nonnegative bounded and continuous function), the results developed in this note are applicable to a class of dynamical systems with uncertain time delays. Finally, a numerical example is given to demonstrate the validity of the results View full abstract»

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  • Self-convergence of weighted least-squares with applications to stochastic adaptive control

    Page(s): 79 - 89
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (844 KB)  

    A recursive least-squares algorithm with slowly decreasing weights for linear stochastic systems is found to have self-convergence property, i.e., it converges to a certain random vector almost surely irrespective of the control law design. Such algorithms enjoy almost the same nice asymptotic properties as the standard least-squares. This universal convergence result combined with a method of random regularization then easily can be applied to construct a self-convergent and uniformly controllable estimated model and thus may enable us to form a general framework for adaptive control of possibly nonminimum phase autoregressive-moving average with exogenous input (ARMAX) systems. As an application, we give a simple solution to the well-known stochastic adaptive pole-placement and linear-quadratic-Gaussian (LQG) control problems in the paper View full abstract»

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  • On applicability of the interacting multiple-model approach to state estimation for systems with sojourn-time-dependent Markov model switching

    Page(s): 136 - 140
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (444 KB)  

    In this paper the attempt at the interacting multiple-model (IMM) method extension to the state estimation problem with semi-Markov [sojourn-time-dependent Markov (STDM)] system model switching is analyzed. It is demonstrated that such an STDM-IMM approach does not properly take into account the specific character of the STDM switching in the system, and it becomes a reason for the reduction of estimation accuracy. For this problem it is shown that a hypotheses merging should be restricted in such a way that not only the current system model, but also the sojourn time in the model, should be given in hypotheses to be tested. Some other aspects of Bayesian estimation in a switching environment are also discussed View full abstract»

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  • The Fornasini-Marchesini and the Roesser models: algebraic methods for recasting

    Page(s): 107 - 112
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    This paper is devoted to giving a new method for recasting the Fornasini-Marchesini model of the two-dimensional system to the Roesser form, endowed with an important feature, that the dimensions of both models are the same. The two-dimensional similarity transformation and spectral transformations of the transfer function variables are used for this purpose. Both the standard and singular cases are considered View full abstract»

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  • On the largest input-output linearizable subsystem

    Page(s): 128 - 132
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    Feedback input-output linearization is considered in this paper. The main result provides the necessary and sufficient conditions to determine the largest dimension of a linear subsystem achievable by a suitable coordinate change after an input-output linearization feedback has been applied. A systematic method to find the desired coordinate change is also given in this paper View full abstract»

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  • Properties of the mixed μ problem and its bounds

    Page(s): 155 - 159
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (556 KB)  

    Upper and lower bounds for the mixed μ problem have recently been developed, and here we examine the relationship of these bounds to each other and to μ. A number of interesting properties are developed and the implications of these properties for the robustness analysis of linear systems and the development of practical computation schemes are discussed. In particular we find that current techniques can only guarantee easy computation for large problems when μ equals its upper bound, and computational complexity results prohibit this possibility for general problems. In this context we present some special cases where computation is easy and make some direct comparisons between mixed μ and “Kharitonov-type” analysis methods View full abstract»

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  • Passive stochastic approximation with constant step size and window width

    Page(s): 90 - 106
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    Motivated by the desire to solve a steady-state estimation and detection problem in chemical engineering, and inspired by the recent progress in passive stochastic approximation, recursive algorithms combining stochastic approximation and kernel estimation are studied and developed in this work. The underlying problem can be stated as finding the roots f(x)=0 provided only noisy measurements yn=f(xnn) are available, where Ef(x, ξn)=f(x). The main difficulty lies in that unlike the traditional approach in stochastic approximation, the sequence {x n} is generated randomly and cannot be adjusted in accordance with our wish. Similar to those used in the decreasing step size algorithms, another sequence {zn} is generated to approximate the roots of f¯(x)=0. Some of the features of the algorithms include: constant step size and constant window width and correlated random processes. Under fairly general conditions, it is proven that a weak convergence result holds for an interpolated sequence of the iterates. Error bounds are obtained and a local limit theorem is also derived. The algorithm is then applied to an estimation problem in chemical engineering. Simulation has shown promising results View full abstract»

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  • A counterexample in power signals space

    Page(s): 115 - 116
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    The present author points out that in the paper by Vidyasagar (1993) on nonlinear system analysis, some of the results obtained are false. The purpose of this paper is to give a counterexample. It is shown that the set of power signals is not a vector space View full abstract»

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  • The marginalized likelihood ratio test for detecting abrupt changes

    Page(s): 66 - 78
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    The generalized likelihood ratio (GLR) test is a widely used method for detecting abrupt changes in linear systems and signals. In this paper the marginalized likelihood ratio (MLR) test is introduced for eliminating three shortcomings of GLR while preserving its applicability and generality. First, the need for a user-chosen threshold is eliminated in MLR. Second, the noise levels need not be known exactly and may even change over time, which means that MLR is robust. Finally, a very efficient exact implementation with linear in time complexity for batch-wise data processing is developed. This should be compared to the quadratic in time complexity of the exact GLR View full abstract»

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  • A multivariable extension of the Tsypkin criterion using a Lyapunov-function approach

    Page(s): 149 - 152
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    For analyzing the stability of discrete-time systems containing a feedback nonlinearity, the Tsypkin criterion is the closest analog to the Popov criterion which is used for analyzing such systems in continuous time. Traditionally, the proof of this criterion is based upon input-output properties and function analytic methods. In this paper we extend the Tsypkin criterion to multivariable systems containing an arbitrary number of monotonic sector-bounded memoryless time-invariant nonlinearities, along with providing a Lyapunov function proof for this classical result View full abstract»

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  • Assigning invariant polynomials over polytopes

    Page(s): 144 - 148
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    This paper provides a parameterization of all output feedback controllers yielding closed-loop invariant polynomials varying over some assigned polytopes View full abstract»

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In the IEEE Transactions on Automatic Control, the IEEE Control Systems Society publishes high-quality papers on the theory, design, and applications of control engineering.  Two types of contributions are regularly considered

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Editor-in-Chief
P. J. Antsaklis
Dept. Electrical Engineering
University of Notre Dame