H ∞ containment control with time‐varying delays and communicate noise under semi‐Markov switching topologies

Abstract

Abstract This article focuses on H ∞ containment control and the communication network topologies that are driven by a semi‐Markov chain. Moreover, the communication channels between agents exist time‐varying delays and noise. Firstly, the authors extend the Markov switching topologies to semi‐Markov switching topologies. Because the transition rate of the semi‐Markov switching topology is time‐varying and depends on the sojourn time, the analysis of containment control under semi‐Markov switching topology becomes more challenging. Secondly, a control protocol with time‐varying delays is adopted. The error function is derived by the property of graph theory, convex hull and communication noise. Hence, the problem of H ∞ containment control is transformed into the stability problem of the semi‐Markov jump system. To avoid the zero initial condition in the traditional H ∞ control approach, a novel performance function is constructed with the initial condition considered. Finally, simulation experiments are provided to verify the effectiveness of the proposed algorithm.

Keywords

• delays
• graph theory
• H∞ control
• Markov processes
• stability
• switching systems (control)