Analysis and design of switched linear systems in the presence of actuator saturation and L∞ disturbances

This paper considers the problem of disturbance tolerance/rejection for a family of linear systems subject to actuator saturation and L_infin disturbances. For a given set of linear feedback gains, a given switching scheme and a given bound on the L_infin 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. With these conditions, both the problem of assessing the disturbance tolerance/rejection capability of the closed-loop system and the design of feedback gain 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 from a given set remain bounded. Disturbance rejection is measured by the L_infin norm of the system output. 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 achieve.