Robust wedge-stability analysis and design of continuous constrained systems with stability radii

In this paper, based on stability radii, a sufficient condition is first proposed to ensure the robust wedge stability of continuous-time constrained systems with state feedback. The saturated actuator is reformulated as a conditioned linear actuator subject to structured uncertainties and then an auxiliary matrix is introduced so that the closed-loop system can be characterized into a scheme of stability radius approach. We also investigate the issue of maximizing complex stability radius subject to a wedge region by state feedback. Through iteratively solving a parametrized Riccati equation, a desired maximizing state feedback controller corresponding to the prescribed wedge subregion can be obtained. An example is given to illustrate the design algorithm and to reveal the feasibility of stability radius approach for continuous-time constrained systems.