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

• DOI: 10.1016/j.ins.2021.03.031
• Publication Date: 2021-03-19T02:39:33Z
• Authors: Chenchen Fan; James Lam; Xiaochen Xie; Xiaoqi Song
• Keywords: Observer (physics)

Abstract 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.