L₂-gain analysis and control synthesis of uncertain switched linear systems subject to actuator saturation

Abstract

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.

Keywords:

• L ₂-gain
• switched systems
• saturating actuators
• disturbance tolerance
• LMI
• multiple Lyapunov functions

Acknowledgements

This work was supported by the NSFC under Grants 60874024 and 90816028 and the SRFDP under Grant 200801450019, by the Ministry of Education of Macedonia under Grant 14-3154/1-17.12.2007 and by Dogus University Fund for Science.