Stability Analysis of Time-Varying Neutral Stochastic Hybrid Delay System
Huabin Chen, Peng Shi, Cheng‐Chew Lim
Abstract
This note analyzes the stochastic stability for time-varying neutral stochastic hybrid delay system, which includes the stability in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$p$</tex-math></inline-formula> th( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$p\geq 2$</tex-math></inline-formula> )-moment, the asymptotical stability in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$p$</tex-math></inline-formula> th( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$p\geq 2$</tex-math></inline-formula> )-moment, the exponential stability in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$p$</tex-math></inline-formula> th( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$p\geq 2$</tex-math></inline-formula> )-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.