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Estimation of sliding mode domains of uncertain variable structure systems with bounded controllers

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3 Author(s)
Madani-Esfahani, S.M. ; Sch. of Electr. Eng., Purdue Univ., West Lafayette, IN, USA ; Hached, M. ; Zak, S.H.

The problem of estimating regions of asymptotic stability (RAS) of uncertain dynamical systems with bounded controllers and the sliding model requirement is discussed. The notion of combining different Lyapunov functions is utilized. Different Lyapunov functions are found, and for each Lyapunov function an estimate of the RAS is found. Different regions are combined in order to find an improved RAS. The combined region is not, in general, a convex region and cannot be found analytically by using just a single Lyapunov function. A class of uncertain, linear, time-invariant, multivariable control systems is considered, and a transformation for decoupling the system into two subsystems is used. The transformation simplifies the RAS estimation problem. Stability domains are estimated for a linear, variable-structure control system with sliding mode performance in the case of a discontinuous bounded controller

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Automatic Control, IEEE Transactions on  (Volume:35 ,  Issue: 4 )