L2-gain analysis and anti-windup design of discrete-time switched systems with actuator saturation

• Published in: International journal of automation and computing Vol. 9; no. 4; pp. 369 - 377
• Main Authors: Zhang, Xin-Quan, Zhao, Jun
• Format: Journal Article
• Language: English
• Published: Heidelberg Institute of Automation, Chinese Academy of Sciences 01.08.2012; Springer Nature B.V
• Subjects: Actuators; CAE) and Design; Closed loops; Compensation; Computer Applications; Computer-Aided Engineering (CAD; Control; Convexity; Design analysis; Discrete time systems; Disturbances; Engineering; L2 gain; Liapunov functions; Linear matrix inequalities; Mathematical analysis; Mechatronics; Regular Papers; Robotics; Upper bounds; saturating actuators; tolerable disturbances; switched systems; switched Lyapunov function; anti-windup; gain
• ISSN: 1476-8186; 2153-182X; 1751-8520; 2153-1838
• DOI: 10.1007/s11633-012-0657-x

This paper investigates L 2 -gain analysis and anti-windup compensation gains design for a class of discrete-time switched systems with saturating actuators and L 2 bounded disturbances by using the switched Lyapunov function approach. For a given set of anti-windup compensation gains, we firstly give a sufficient condition on tolerable disturbances under which the state trajectory starting from the origin will remain inside a bounded set for the corresponding closed-loop switched system subject to L 2 bounded disturbances. Then, the upper bound on the restricted L 2 -gain is obtained over the set of tolerable disturbances. Furthermore, the antiwindup compensation gains aiming to determine the largest disturbance tolerance level and the smallest upper bound of the restricted L 2 -gain are presented by solving a convex optimization problem with linear matrix inequality (LMI) constraints. A numerical example is given to illustrate the effectiveness of the proposed design method.