Exponential stability and L1-gain performance analysis for continuous-time delayed switched positive singular systems

Abstract

The problem of exponential stability and L1-gain performance is solved for continuous-time delayed switched positive singular systems. First, a necessary and sufficient condition of positivity is established for the system via the singular value decomposition approach. Then, based on the co-positive Lyapunov function tool, we develop a sufficient condition for the switched positive singular system to be exponentially stable and meet a prescribed L1-gain performance. Based on this condition, the optimal system performance level can be determined by solving a convex optimization problem. All the obtained conditions are in linear programming form, which suggests a good scalability and applicability to high-dimensional systems. Finally, a numerical example is given to illustrate the applicability of the obtained results.