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Estimation of stability regions for linear systems subjected to actuator saturation and disturbance via homogeneous parameter-dependent quadratic Lyapunov functions

In this paper, the problems of analysis and design for linear systems subjected to actuator saturation and disturbance are addressed by using homogeneous parameter-dependent quadratic Lyapunov functions. The condition and feedback matrices which determine if the set is strictly invariant are derived. Based on this condition, the problems which determine the invariant sets for systems with persistent disturbance can be expressed as linear matrix inequalities (LMIs) optimization problem. By solving these LMIs optimization problems. We know that this method reduce conservatism than the existing methods. Finally, numerical examples illustrate the effectiveness of our method.