Design of switched linear systems in the presence of actuator saturation and L-infinity disturbances

Abstract

This paper considers the problem of disturbance tolerance/rejection of a switched system resulting from a family of linear systems subject to actuator saturation and L-infinity disturbances. For a given set of linear feedback gains, a given switching scheme and a given bound on the L-infinity norm of the disturbances, conditions are established, in terms of linear or bilinear matrix inequalities, under which a set of a certain form is invariant for a given switched linear system in the presence of actuator saturation and L-infinity disturbances, and the closed-loop system possesses a certain level of disturbance rejection capability. With these conditions, the design of feedback gains and switching scheme can be formulated and solved as constrained optimization problems. Disturbance tolerance is measured by the largest bound on the disturbances for which the trajectories starting from a given set remain bounded. Disturbance rejection is measured either by the L-infinity norm of the system output or by the system’s ability to steer its state into and/or keep it within a small neighborhood of the origin. In the event that all systems in the family are identical, the switched system reduces to a single system under a switching feedback law. Simulation results show that such a single system under a switching feedback law could have stronger disturbance tolerance/rejection capability than a single linear feedback law can.