Finite-Time Stabilization of Markov Switching Singularly Perturbed Models

This brief is concerned with the issue of finite-time stabilization of discrete-time stochastic singularly perturbed models, in which the stochastic process is regulated by a Markov chain with partially unknown transition probabilities (TPs). The slow-state and fast-state variable are considered in the modeling, and the corresponding Markov switching model with a singularly perturbed parameter is obtained in a unified framework. Ill-conditioned problems caused by a small singular perturbation parameter are prevented by developing a finite-time stability criterion for the resultant system. Furthermore, feasible conditions are derived for the desired finite-time state feedback controller by using matrix inequalities that are independent of the singularly perturbed parameter. Finally, a gear-driven DC motor model is applied to illustrate the effectiveness of the described control strategy.

Automated summary

This brief discusses the issue of finite-time stabilization of discrete-time stochastic singularly perturbed models, where the stochastic process is regulated by a Markov chain with partially unknown transition probabilities. The paper considers the slow-state and fast-state variables and obtains a Markov switching model with a singularly perturbed parameter in a unified framework. It develops a finite-time stability criterion to prevent ill-conditioned problems caused by a small perturbation parameter and derives feasible conditions for the desired finite-time state feedback controller using matrix inequalities that are independent of the perturbation parameter. The effectiveness of the control strategy is illustrated using a gear-driven DC motor model.