L ₂-gain analysis and control synthesis of uncertain switched linear systems subject to actuator saturation

This article addresses the L ₂-gain analysis and control synthesis problem for a class of uncertain switched linear systems with saturating actuators and external disturbances. First, when the controllers are pre-given, an analysis condition on disturbance tolerance is established under which the state trajectory starting from the origin will remain inside a bounded set. By this condition, the problem of estimating disturbance tolerance capability is formulated as a constrained optimisation problem. Then, the restricted L ₂-gain property is analysed over the set of tolerable disturbances. An upper bound on the restricted L ₂-gain is estimated by solving a constrained optimisation problem. Furthermore, when controller gain matrices are design variables, these optimisation problems can be adapted for controller design. All the results are achieved by utilising the multiple Lyapunov functions method and presented in terms of an LMI optimisation-based approach. A numerical example is given to show the effectiveness of the proposed method.