Robust passivity analysis of Markov‐type Lotka–Volterra model with time‐varying delay and uncertain mode transition rates

Abstract

This paper devotes to the global robust passivity problem for a novel Markovian switching Lotka–Volterra (LV) model with time‐varying delay. The Markovian switching with uncertain mode transition rates is first drawn into modeling the predator–prey system and the uncertainty of model parameters is also fully discussed, which can reflect the realistic practical significance. The robust passivity for the uncertain LV model with disturbance input and feedback control is studied by the passivity theories and inequality techniques. Some sufficient criteria are derived by the Lyapunov–Krasovskii functional, and the corresponding controllers are designed to ensure the passivity of the proposed closed‐loop uncertain LV model. Finally, a three‐specie two‐mode LV model is provided to illustrate effectiveness of the proposed theoretical results.