Absolute Exponential Stability for Switching Positive Systems With Time-Delay Based on the Φ-Dependent ADT Strategy

Abstract

The absolute exponential stability problem for the continuous-time and discrete-time, respectively, switching positive nonlinear time-delay system is investigated under the nonlinearity of systems satisfying a certain sector condition in this paper. Two multiple co-positive Lyapunov-Krasovskii functionals (MCLKF) of such systems are constructed for the continuous-time and discrete-time contexts respectively. By using the MCLKF and the $\Phi $ -dependent average dwell time switching strategy, more general stability conditions compatible with some existing works are established. Furthermore, the obtained results are generalized to other types of systems. A numerical example, finally, implies the validity and significance of the results proposed.

Keywords

• Switching positive systems
• absolute exponential stability
• average dwell time
• Lyapunov-Krasovskii functional