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Robust stability analysis for uncertainty linear systems with state saturation

In this paper, the robust stability of an uncertain continuous linear system with state saturation is investigated, where the uncertain matrices are assumed to satisfy convex-polyhedron structures. Firstly, a linearized formulation of the state saturation function is established by means of a semipositive (seminegative) set. Secondly, the sufficient conditions of the global asymptotic stability are given by using a Lyapunov function for full and partial state saturation systems on the origin respectively. Furthermore, the corresponding algorithms are designed to achieve the decision of the sufficient conditions. Finally, the validity of the conditions obtained above is verified through two numerical experiments.