Passivity-based finite-region control of 2-D hidden Markov jump Roesser systems with partial statistical information

The problem of the finite-region passive control for 2-D Markov jump Roesser systems, in which the partial statistical information issues on Markov parameters and transition probabilities are considered simultaneously. To model this situation, a 2-D hidden Markov model with partial statistical information is established. The purpose of this paper is to design a controller based on the 2-D hidden Markov model such that both the horizontal states and vertical states of 2-D Markov jump Roesser systems are bounded in finite-time and a passive performance is met. Based on the Lyapunov function method, the criteria for the finite-region boundedness of 2-D Markov jump Roesser systems are established and the design method of the 2-D hidden Markov model-based asynchronous controller is presented. The effectiveness of the design method is verified by an illustrative example.

Automated summary

This paper addresses the problem of finite-region passive control for 2-D Markov jump Roesser systems, considering the partial statistical information issues on Markov parameters and transition probabilities. A 2-D hidden Markov model with partial statistical information is established to model this situation. The goal is to design a controller based on the 2-D hidden Markov model that ensures finite-time boundedness of both horizontal and vertical states of the 2-D Markov jump Roesser systems, while meeting a passive performance criterion. By employing the Lyapunov function method, criteria for the finite-region boundedness of 2-D Markov jump Roesser systems are developed, and a design method for the asynchronous controller based on the 2-D hidden Markov model is presented. The effectiveness of the proposed design method is validated through an illustrative example.