H∞ Control for a Class of Continuous-time Switched Systems with State Constraints

• Published in: Asian journal of control Vol. 16; no. 2; pp. 451 - 460
• Main Authors: Su, Qingyu, Zhao, Jun
• Format: Journal Article
• Language: English
• Published: Hoboken Blackwell Publishing Ltd 01.03.2014; Wiley Subscription Services, Inc
• Subjects: Closed loop systems; Control theory; H∞ control; improved average dwell time; state constraints; Switched systems; Switching
• ISSN: 1561-8625; 1934-6093
• DOI: 10.1002/asjc.706

This paper investigates the H∞ control problem for a class of continuous‐time switched systems subject to state constraints with an improved average dwell time. The state constraints are converted into state saturations by limiting the state in a unit hypercube. By employing this proposed improved average dwell time method, which takes into account different decay rates of a Lyapunov function related to an active subsystem according to whether the saturations occur or not, the resulting minimum of admissible average dwell time is smaller than the one of the standard average dwell time, which only considers the same decay rate regardless of whether the saturations occur or not. In addition, switched state feedback controllers are designed such that the closed‐loop switched system, subject to state constraints, is asymptotically stable and achieves a weighted L2‐gain. Sufficient conditions for H∞ control of the switched system with state constraints are derived before an application to a Pulse‐Width‐Modulation (PWM)‐driven boost converter is given to illustrate the applicability and the effectiveness of the proposed method.