Robust Reliability as a Measure of Stability of Controlled Dynamic Systems with Bounded Uncertain Parameters

Abstract

Based on an appropriate uncertainty description, a new robust reliability method for stability issue of dynamic systems is developed to deal with bounded uncertainties. The presented methods provide necessary and sufficient conditions for quadratic stability and stabilization of uncertain systems and are suitable both for cases where the bounds of uncertain parameters are known and where they are unknown. Using this method, a robust reliability measure of the stability of parametric uncertain systems can be provided, and the maximum robustness bounds of uncertain parameters such that the system can be stable can be obtained. The design of a controller for stabilizing uncertain systems is carried out by solving a robust-reliability-based convex optimization problem. This makes it possible to take both the robustness with respect to uncertainties and the control cost into account simultaneously in the controller design. Moreover, the presented procedures are within the framework of linear matrix inequality and can be implemented conveniently. Two examples are provided to demonstrate the effectiveness and feasibility of the proposed methods. By numerical simulations and compared with existing results, it is shown that increasing conservatism in controller design by traditional methods does not mean increasing reliability, and so it is significant to take the robust reliability into account in the controller design of uncertain systems.