Polynomial Stability of Stochastic Switched Systems Based on Lyapunov‐Halanay Function and Lyapunov‐Krasovskii Functional

ABSTRACT This paper investigates the ‐th moment polynomial stability of stochastic switched systems. By constructing decay‐type and growth‐type Lyapunov–Halanay functions and Lyapunov–Krasovskii functionals, a novel compatibility condition between the adopted functions and functionals is established. Different from the traditional average dwell‐time scheme, this paper abandons the strict dwell‐time constraint and only imposes reasonable restrictions on the switching number and the occupation time ratio of decay and growth modes. Three sets of progressive sufficient stability criteria are further derived, which are applicable to systems with pure decay‐type Lyapunov–Halanay conditions, pure decay‐type Lyapunov–Krasovskii conditions, and mixed decay–growth operating modes, respectively. Finally, numerical simulations on linear and nonlinear stochastic systems are presented to validate the correctness, flexibility and superiority of the derived theoretical results.