Stability analysis of linear systems under state and rate saturations

In this paper, we provide a stability analysis for linear systems which have simultaneous saturations in the states and their rates (dynamics). The stability analysis is conducted via a formulation based on the polytopic representations of two saturation functions, state and rate saturation functions. Sufficient conditions to guarantee local and global asymptotical stability of such systems are derived. Furthermore, using the invariance analysis, we estimate the domain of attraction of the system when it is locally asymptotically stable. The stability conditions are formulated as an iterative LMI (ILMI) algorithm. Finally, numerical examples are presented to validate the proposed method.