Practical Exponential Stability of Positive Switched Linear System and Its Application in Practical Consensus of Multi-agent System

In this technical note, we investigate the practical exponential stability of a positive switched linear system with impulses and all subsystems unstable. By constructing two types of switched discretized Lyapunov functions, we give some new sufficient conditions such that the system achieves practical exponential stability under mode-dependent range dwell time switching. Following this, we apply these results to the practical consensus of multi-agent system under switching topologies. The mathematical analysis is validated by a set of numerical examples.