Robust Observer-Based Adaptive High-Gain Feedback Design for Uncertain Saturated Discrete-Time Linear Systems

This paper aims at designing an adaptive robust observer-based feedback controller for uncertain and saturated discrete-time linear systems. The uncertainties and the saturation are included in convex hulls and a Lyapunov function is used to ensure stability of the closed loop. By using an iterative algorithm, the controller and observer gains are computed simultaneously using LMI techniques. The method derives a sequence of controllers which gains have an increasing Frobenius norm when the control errors decrease. In this context, two methods for time-varying controllers are presented: a switching algorithm and an interpolation method. The parameter settings and the control performance are discussed using a numerical example and a payload crane system.