H_∞ filtering of discrete‐time switched singular systems with time‐varying delays

Abstract

Summary In this article, the analysis and design problems of H∞ filtering for a class of discrete‐time switched singular systems with time‐varying delay under an arbitrary switching signal are investigated. The main attention is focused on the design of a linear mode‐dependent filter guaranteeing the regularity, causality, and asymptotic stability of the resulting filtering error system with a prescribed H∞ performance bound. By using a multiple Lyapunov‐Krasovskii functional, and utilizing the linearization technique, novel sufficient conditions for the solvability of H∞ problem are derived in terms of linear matrix inequalities. Solving that, the desired filter gains can be determined. Any model transformation of system, which often leads the large computational burden is involved. The free weighting matrix technique is introduced to provide additional degree of freedom, which improves the conservativeness of the developed method. Finally, numerical examples are given to demonstrate the effectiveness and the merit of the proposed approach and to compare the obtained results with some previous works in the literature.

Event‐triggered quantized‐output state estimation for discrete singular Markovian jump systems

“…It is worth noting that the system regularity and impulse-free properties are necessary to be checked when considering this class of system model. [1][2][3][4] Moreover, singular systems are extensively affected by abrupt changes in their structure owing to a variety of phenomena such as component failures, and thus those systems are known as singular systems with Markovian jump parameters. Despite their complexity, much challenging work has been tackled for singular Markovian jump systems.…”

Output regulation for switched singular systems based on a reduced‐order error feedback controller

“…And the disturbance decoupling with stability for switched systems has been considered Reference 19. In practical applications, when the components of the power systems and complex network systems fail or recover, the external environment of the biological information systems or chemical reaction processes change, the demand of the economic system changes, they can be modeled by switched singular systems 20 . In addition, switched singular systems are widely applied in aircraft systems and restricted robot systems.…”

Guaranteed cost finite-time control of large-scale singular systems with interconnected delays

“…When studying the stability and control of singular systems, an aspect to be considered is ensuring the admissibility, that is, the regularity, impulse-absence and stability of the system. Moreover, in suboptimal control problems, such as H ' control and guaranteed cost control, it is desirable to design feedback controllers guaranteeing not only the admissibility of the system, but also an adequate level of system performance (Boukas, 2011;Chaibi et al, 2021;Charqi et al, 2020;Sheldon et al, 1972;Wei et al, 2019). Various interesting results of this problem have been presented (Fridman and Shaked, 2005;Khongja et al, 2018;Kwon and Park, 2006;Thuan et al, 2019;Wang et al, 2012), where there were sufficient conditions for designing guaranteed cost controllers of large-scale systems with delays; however, the singularity was not addressed in these papers.…”