Robust H∞ guaranteed cost control for discrete‐time switched singular systems with time‐varying delay

• Published in: Optimal control applications & methods Vol. 40; no. 1; pp. 119 - 140
• Main Authors: Regaieg, Mohamed Amin, Kchaou, Mourad, El Hajjaji, Ahmed, Chaabane, Mohamed
• Format: Journal Article
• Language: English
• Published: Glasgow Wiley Subscription Services, Inc 01.01.2019; Wiley
• Subjects: Automatic; Control stability; Control systems design; Controllers; Delay; delay partitioning; Dwell time; Electric power; Engineering Sciences; Feedback control; H-infinity control; LQ cost; Mathematical analysis; Matrix methods; mode‐dependent average dwell time; Output feedback; Robust control; Robustness (mathematics); switched singular systems; Time dependence; time‐varying delay; Upper bounds
• ISSN: 0143-2087; 1099-1514
• DOI: 10.1002/oca.2470

Summary This paper investigates the problem of control design for a class of uncertain switched singular systems with time‐varying delay. Under mode‐dependent average dwell time and using an appropriate Lyapunov‐Krasovskii functional, the exponential admissibility of the system is analyzed. In order to obtain less conservative conditions, the delay partitioning technique is adopted as well as the improved reciprocally convex approach. By means of the developed admissibility condition, a static output feedback controller is then designed using linear matrix inequality approach. Moreover, by solving an optimization convex problem with constraints, the switched controller is developed to ensure simultaneously the stability of the closed‐loop system and satisfy an optimized upper bound of both the linear quadratic guaranteed cost and the H∞ norm. Numerical examples are proposed to verify the efficiency and the merits of the method proposed.