Stability of stochastic delayed multi-links complex network with semi-Markov switched topology: A time-varying hybrid aperiodically intermittent control strategy

Abstract

This paper is concerned with the stability analysis of stochastic delayed multi-links complex networks with semi-Markov switched topology (SDMNST). It ought to be highlighted that a time-varying hybrid aperiodically intermittent control (THAIC) strategy, that the control gain is a sign-indefinite function and can be unbounded, is proposed. In the light of a major consideration for both stabilizing control and destabilizing input, the THAIC is capable of being manipulated to a wider range of intermittent control signals. Meanwhile, our proposed control strategy can not only deal with the problem that the intermittent control signals subject to external interferences, but also effectively avoid the possible damage of actuators caused by the sudden and rapid switching of control gain from a negative constant value to zero. The concept “average intermittent control gain” is introduced to quantify the gain of THAIC. As a generalization of the existing Halanay-type inequalities, several novel differential inequalities with time-varying and unbounded coefficients are established, based on which and Lyapunov method as well as graph theory, less conservative stability criteria of SDMNST are rigorously demonstrated. Subsequently, the theoretical results are applied to spring-mass-damper systems and numerical simulations are exploited with the design of control gain being shown.