Reachable set estimation and controller design for discrete‐time singularly perturbed systems with time‐varying delay

Abstract

In this article, we study the reachable set estimation and controller design problems for a class of discrete time-varying-delay singularly perturbed systems. First, by constructing a -dependent Lyapunov-Krasovskii functional and using reciprocally convex inequality, delay-dependent conditions are obtained to ensure the state of the system under zero initial conditions is contained by an ellipsoid for any singularly perturbed parameters below a given threshold.Second, by the method of designing a state-feedback controller, sufficient conditions that the reachable set of the closed-loop system can be included in a given ellipsoid are obtained for admissible singularly perturbed parameters. Finally, two examples are given to illustrate the effectiveness of the results.

Enclosing ellipsoid‐based reachable set estimation for discrete‐time singular systems

“…Proof. The coordinates of the system (1) is transformed by applying ( 8) and (10), that is, the system (1) is decomposed into (11).…”

“…Therefore, reachable set estimation has been investigated for many different systems during the past decade. [5][6][7][8][9][10] For instance, Zuo et al 11 study reachable set estimation for linear delayed systems subject to polytopic uncertainties; Che et al 12 focus on the research of nonfragile and nonsynchronous synthesis for Bernoulli switched systems with unknown but mean square peak bounded disturbance; Chen et al 13 investigate the problems of reachable set estimation and synthesis for periodic positive systems.…”

State bounding and controller design for genetic regulatory networks with multiple delays and bounded disturbances

“…The reachable set estimation and decentralized control synthesis problems for large-scale switched systems under mixed switching were investigated in Reference 45. In addition, the reachable set estimation and controller design problems had been considered for nonlinear systems with time-varying delay, 46 periodic positive systems, 47,48 delta operator systems, 49 singularly perturbed systems, 50 and switched neutral systems. 51 However, no result about the state bounding for GRNs with both discrete and distributed time delays has been reported, which is the first motivation for this article.…”