Stability Analysis of Time-Varying Neutral Stochastic Hybrid Delay System

This note analyzes the stochastic stability for time-varying neutral stochastic hybrid delay system, which includes the stability in
$p$
th(
$p\geq 2$
)-moment, the asymptotical stability in
$p$
th(
$p\geq 2$
)-moment, the exponential stability in
$p$
th(
$p\geq 2$
)-moment, and the almost surely exponential stability. One modified version of generalized delay integral inequality, the Lyapunov–Krasovskii function, and the stochastic analysis are used. The proposed methodology can surmount the analytical difficulty, which stems from the coexistence of neutral term, stochastic disturbance, bounded time-varying delay, and a sign-changed time-varying coefficient in the diffusion condition. An example is given to show the effectiveness of the theoretical results obtained.