Robust stabilization of switched positive discrete‐time systems with asynchronous switching and input saturation

• Published in: Optimal control applications & methods Vol. 40; no. 1; pp. 105 - 118
• Main Authors: Zhang, Yong, Hu, Jingjing, Liu, Dexiang, Xia, Debao
• Format: Journal Article
• Language: English
• Published: Glasgow Wiley Subscription Services, Inc 01.01.2019
• Subjects: asynchronous switching; Control stability; Control systems; Controllers; Discrete time systems; Dwell time; Feedback control; input saturation; l1‐gain performance; mode‐dependent average dwell time; Robust stabilization; Saturation; stabilization; State feedback; Subsystems; switched positive system; Switching; Time dependence; Time varying control systems
• ISSN: 0143-2087; 1099-1514
• DOI: 10.1002/oca.2469

Summary This paper investigates the stabilization problems of switched positive discrete‐time systems with asynchronous switching and input saturation jointly. The asynchronous switching means that state feedback controllers lag behind the subsystems for a period. Next, the input saturation comes from the saturation effect of state feedback controllers. In this paper, the exponential stability condition is firstly obtained based on mode‐dependent average dwell time method. Then, under zero initial condition, we analyze the boundedness and l1‐gain performance of the system with disturbance. Finally, considering that state feedback controllers for some subsystems cannot be designed, we study the exponential stability condition of the system with unstable subsystems. Moreover, optimization methods are given to get the optimal solution to the nonlinear inequality constraints.