Exponential Stability and ℒ1-Gain Performance for Positive Sampled-Data Control Systems

This paper aims to explore the application of sampling control technology in positive Markov jump systems (PMJSs), focusing on the exponential stability in mean and L1-gain performance of the system. We first establish a PMJS model based on sampling control and conduct a detailed analysis of its exponential stability in mean. Subsequently, combined with L1-gain theory, we propose a sufficient condition for PMJSs with a prescribed L1-gain performance level, which ensures the robustness and satisfaction of performance indicators of the system in a randomly switching environment. From the sufficient conditions we have given, we can indeed see the effect of the sampling period on the system performance. Based on this sufficient condition, we further design the state feedback controller, and give the feedback gain solving algorithm based on linear programming method. A simple simulation example verifies the correctness and effectiveness of the results. The main contribution of this paper is to introduce sampling control technology into the research of PMJSs and propose a complete theoretical framework and analysis method, providing new theoretical support and practical application value for the sampling control of PMJSs.