Robust stability and H_∞ control for nonlinear discrete‐time switched systems with interval time‐varying delay

Abstract

This paper considers the problems of the robust stability analysis and H∞ controller synthesis for uncertain discrete‐time switched systems with interval time‐varying delay and nonlinear disturbances. Based on the system transformation and by introducing a switched Lyapunov‐Krasovskii functional, the novel sufficient conditions, which guarantee that the uncertain discrete‐time switched system is robust asymptotically stable are obtained in terms of linear matrix inequalities. Then, the robust H∞ control synthesis via switched state feedback is studied for a class of discrete‐time switched systems with uncertainties and nonlinear disturbances. We designed a switched state feedback controller to stabilize asymptotically discrete‐time switched systems with interval time‐varying delay and H∞ disturbance attenuation level based on matrix inequality conditions. Examples are provided to illustrate the advantage and effectiveness of the proposed method.

Robust model predictive control of uncertain nonlinear time‐delay systems via control contraction metric technique

“…In most cases, such phenomena might deteriorate the dynamic performance of systems, or even lead to instability. Regarding this problem, extensive research has been devoted to the robust control of uncertain time‐delay systems 1‐11 …”

Robust observer-based finite-time $H_{\infty}$ control designs for discrete nonlinear systems with time-varying delay

“…Feedback control is a long-standing topic and has been one of the key research areas in control theory [7,8,16]. State feedback control is developed on the premise that the complete state information of the system is available.…”

Observer-based robust model predictive control of switched nonlinear systems with time delay and parametric uncertainties

“…Because of the existence of uncertainties in most realworld systems, the stability analysis of uncertain time-delay switched systems is of practical importance. Literature searches reveal that polytopic and norm-bounded uncertainties have been considered more for uncertain timedelay switched systems (Dong et al, 2019;Zhang et al, 2007). However, a parametric uncertainty is more compatible with practical systems and leads to less conservative analysis and less computational burden than the other types of uncertainties (Baleghi and Shafiei, 2018c).…”