Novel Delay-Dependent Stability Criteria for Time-Varying Stochastic Delay Systems with Markovian Switching

The
$p-th$
moment stability analysis of time-varying stochastic delay systems with Markovian switching is investigated in this paper. By the method based on the Lyapunov function and some inequality techniques, two novel stability criteria are obtained to ensure the uniform stability in
$p-th$
moment and uniform exponential stability in
$p-th$
moment of the studied systems. The established results are characterized by the time-varying coefficients in the time-derivatives of the Lyapunov function being allowed to be unbounded. This is less conservative because the norm of the time-varying coefficients of the state variables and retarded state variables of the system under study is allowed to be unbounded. The last some examples are provided to illustrate the effectiveness and superiority of the proposed theoretical results.