Non-quadratic Lyapunov functions for performance analysis of saturated systems

In a companion paper [14], we developed a systematic Lyapunov approach to the regional stability and performance analysis of saturated systems via quadratic Lyapunov functions. The corresponding conditions are expressed in terms of LMIs but can be too conservative in some cases. To obtain less conservative conditions, we use in this paper two types of conjugate Lyapunov functions: the convex hull quadratic function and the max quadratic function. These functions yield bilinear matrix inequalities (BMIs) as conditions for stability and guaranteed performance level. The BMI conditions cover the LMI conditions for quadratic stability as special cases and hence the reduction of conservativeness is guaranteed. A numerical example demonstrates the effectiveness of this paper’s methods and the great potential of the non-quadratic Lyapunov functions.