Observer-based output reachable set synthesis for periodic piecewise time-varying systems

In this paper, the output reachable set synthesis problem for periodic piecewise time varying systems has been addressed for the first time. Generalized periodic time-varying conditions of the closed-loop system to guarantee the system output bounded by a collection of finite ellipsoids are developed. The decoupling of time-varying observer and controller gains is achieved by a technical lemma. Moreover, by using time-varying matrix functions in multiple linear-interpolative forms and the relaxed quadratic matrix polynomial definiteness results, sufficient condition is developed to determine the periodic time varying observer and controller with reduced conservatism. A tractable iterative algorithm is proposed to obtain the periodic time-varying observer and controller gains. A numerical example is presented to illustrate the validity of proposed methods. (c) 2021 Elsevier Inc. All rights reserved.

Automated summary

This paper addresses the output reachable set synthesis problem for periodic piecewise time-varying systems for the first time, developing sufficient conditions for periodic time-varying observer and controller with reduced conservatism. An iterative algorithm is proposed to obtain the periodic time-varying observer and controller gains, and a numerical example is presented to illustrate the validity of the proposed methods.