Reachable set estimation for switched positive systems

Abstract

This paper focuses on the problem of reachable set estimation for discrete-time switched positive systems under two possible classes of exogenous disturbance. The multiple linear copositive Lyapunov function approach is applied to determine the bounding hyper-pyramids for the reachable set. Based on some Lyapunov-based inequalities and the linear version of the S-procedure technique, the bounding hyper-pyramids for the reachable set can be determined by solving a set of inequalities. Two optimisation methods are adopted to make the bounding hyper-pyramids as small as possible. Genetic Algorithm (GA) is utilised to search for the optimal value of the decision variables in the obtained inequalities. Finally, numerical examples are given to illustrate the effectiveness of the theoretical findings.