Model reduction for discrete-time switched linear time-delayed systems with finite-frequency specifications

The paper focusses on the model reduction of discrete-time switched linear systems with finite-frequency specifications. First, we propose a performance index that can estimate systematic performance over finite frequency. And then, we use GKYP (generalized Kalman–Yakubovich–Popov lemma) and introduce some relaxation matrices with variable parameters to analyse the problem in different situations. Based on the above conditions, sufficient conditions can be obtained for meeting the index of finite frequency. Finally, we illustrate two numerical examples. The results show that the proposed method can improve approximation performance.

Robust sliding mode preview control for uncertain discrete-time systems with time-varying delay

This article focuses on the problem of robust sliding mode preview control for a class of non-linear delayed systems. It is assumed that the reference signal is previewed with a fixed length ahead and the norm of uncertainty is bounded. A model transformation is introduced to approximate the time-varying delay such that augmented error systems can be constructed. Conditions of asymptotic stability of sliding motion are established via the small gain theorem. The sliding mode preview controller is designed such that the controlled system state can be attracted to the switching surface and keep on it thereafter. A numerical example is presented to illustrate the effectiveness of the proposed control design.