Analysis of the region of attraction for saturating control systems-in consideration of the direct-feedthrough matrix from output to input of saturations

This paper proposes two regional stability conditions, equivalently analysis conditions of the region of attraction, for linear time-invariant (LTI) systems with saturations. We consider two analysis approaches in order to derive the conditions. One is an extension of the condition of Park and Choi (2001) in the case of nonzero direct-feedthrough matrix from output to input of the saturation. The other is a transformation from the condition for discrete time systems to a condition for continuous time systems. Finally, we show that the derived conditions are less conservative than the existing results by numerical examples.