Asynchronous Guaranteed Cost Control of 2-D Markov Jump Roesser Systems

This article is concerned with the problem of guaranteed cost control for 2-D Markov jump Roesser systems with mismatched modes. The hidden Markov model is introduced to describe the asynchronous phenomenon caused by mismatched modes, and an asynchronous linear state-feedback control law is designed based on this model. With the help of the 2-D Lyapunov function and linear matrix inequality (LMI) techniques, sufficient conditions are established to ensure the asymptotic stability of the concerned system with a bound of the predefined guaranteed cost under three different boundary conditions, respectively. Finally, an algorithm that concludes the design processes of the optimal asynchronous guaranteed cost control law is proposed, and a numerical example is provided to verify its effectiveness.

Automated summary

This article focuses on the guaranteed cost control for 2-D Markov jump Roesser systems with mismatched modes. It introduces a hidden Markov model to address the asynchronous phenomenon caused by mismatched modes and designs an asynchronous linear state-feedback control law. By utilizing 2-D Lyapunov function and LMI techniques, sufficient conditions are established to ensure system stability and guaranteed cost under different boundary conditions. An algorithm for the optimal asynchronous guaranteed cost control law design is proposed, with a numerical example to validate its effectiveness.