L2-gain analysis and anti-windup design of switched linear systems subject to input saturation

The problem of L2-gain analysis and anti-windup compensation gains design is studied for a class of switched linear systems with actuator saturation via the multiple Lyapunov functions approach. When a set of anti-windup compensation gains are given, a sufficient condition on tolerable disturbances is obtained, under which the state trajectory starting from the origin will remain inside a bounded set. Then over this set of tolerable disturbances, we obtain the upper bound of the restricted L2-gain. Furthermore, the anti-windup compensation gains and the switched law, which aim to determine the maximum disturbance tolerance capability and the minimum upper bound of the restricted L2-gain, are presented by solving a convex optimization problem with linear matrix inequality LMI constraints. Finally we give a numerical example to demonstrate the effectiveness of the proposed method.

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