Disturbance Tolerance and Rejection of Linear Systems with Imprecise Knowledge of Actuator Input Output Characteristics

In this paper, we study the robustness of linear systems with respect to the disturbances and the uncertainties in the actuator input output characteristics. Disturbances either bounded in energy or bounded in magnitude are considered. The actuator input output characteristics are assumed to reside in a so-called generalized sector bounded by piecewise linear curves. Robust bounded state stability of the closed-loop system is first defined and characterized in terms of linear matrix inequalities (LMIs). Based on this characterization, the evaluation of the disturbance tolerance and disturbance rejection capabilities of the closed-loop system under a given feedback law is formulated into and solved as optimization problems with LMI constraints. The maximal tolerable disturbance is then determined by optimizing the disturbance tolerance capability of the closed-loop system over the choice of feedback gains. Similarly, the design of feedback gain that maximizes the disturbance rejection capability of can be carried out by viewing the feedback gain as an additional free parameter in the optimization problem for the evaluation of the disturbance rejection capability under a given feedback gain.