Diagonal Stability Analysis of Discrete-Time Nonlinear Positive Switched Systems with Delays: A Homogeneous Polynomial Diagonal Lyapunov Function Method

This paper addresses the diagonal stability problem of a class of discrete-time nonlinear positive switched systems with delays. Different from previous methods, we first use homogeneous polynomial Lyapunov function method to present the diagonal stability condition of the corresponding linear system of the original nonlinear system, and then use the comparison method to establish its relationship with the nonlinear system. so as to obtain the final result. Finally, a numerical example is provided to illustrate the theoretical results obtained in this paper.