Augmented Lyapunov function approach to ^L2 gain analysis for discrete-time systems with saturation nonlinearities

This paper presents a method for ^L2 gain analysis of discrete-time systems with saturation nonlinearity by using an augmented Lyapunov functional. By using sector and slope properties of the saturation nonlinearity, the ^L2 gain performance criterion is obtained via LMI formulation. The proposed Lyapunov function have augmented quadratic form with states as well as the sector bounded nonlinear function. Numerical examples show that the proposed method is less conservative than the existing ones.