Polynomial Stabilization of Highly Nonlinear Stochastic Systems with Pantograph Delay and Markovian Switching
摘要
In this paper, the authors address the problem of almost sure polynomial stabilization for a class of highly nonlinear stochastic systems via sampled-data feedback. The considered systems fall within a general framework that includes two key features: (a) Continuous-time irreducible Markov chain- the authors introduce a continuous-time irreducible Markov chain to describe systems that can undergo sudden alterations in their parameters and structures. This flexibility allows us to model real-world scenarios more accurately; (b) Diffusion and drift coefficients with polynomial growth - unlike existing literature that primarily focuses on systems with bounded delays, the authors investigate the stabilization conditions for highly nonlinear stochastic systems with pantograph delay, an unbounded delay. Specifically, the authors analyze systems where the diffusion and drift coefficients satisfy a polynomial growth condition. To achieve the proposed goal, the authors employ M-matrix theory and Lyapunov functions as basic tools. The main results establish that the system can attain almost sure polynomial stabilization through a subtly and innovatively designed sampled-data feedback. The authors validate the theoretical findings with numerical simulations, demonstrating the effectiveness of the proposed approach. This work contributes to the understanding of stabilization in highly nonlinear stochastic systems, particularly those with unbounded delays, and broadens the practical applicability of stochastic modeling.