Exponential Stability of Dynamical Systems on Time Scales with Application to Multi-Agent Systems

Abstract

The exponential stability criteria of systems with time delays on time scales are established, which unifies and generalizes the continuous and discrete cases. The time derivatives of Lyapunov functions (functionals) along solutions are allowed to be indefinite, namely, to take both negative and positive value, which reduces conservatism of the criteria. Moreover, the stability criteria are applicable to both linear and nonlinear systems on time scales, which expands the scope of application of the criteria. Furthermore, the improved stability theorem is applied to solve a leader-following consensus problem of multi-agents on time scales. Sufficient conditions are derived for the leader-following consensus of multi-agent systems under directed interaction topology. A numerical example is given to illustrate the feasibility and effectiveness of the theoretical results.