H∞ Control of Markovian Jump Linear Singularly Perturbed Systems

This paper studies H infinity control of Markovian jump linear singularly perturbed systems (MJLSPSs). A sufficient condition in terms of linear matrix inequalities (LMIs), different from ones in previous existing works, is given for designing H infinity control to overcome the difficulties of solving either Riccati equations or nonlinear matrix inequalities. Then, the jump H infinity controller can be obtained effectively by solving the proposed LMIs. Furthermore, a method is developed for evaluating an allowable upper bound of the singular perturbation parameter, in which a prescribed H infinity performance is satisfied. Finally, two numerical examples are presented to illustrate the effectiveness of the proposed design methods.

Automated summary

This paper focuses on the H infinity control of Markovian jump linear singularly perturbed systems, providing a new sufficient condition based on linear matrix inequalities. The proposed method aims to effectively design the jump H infinity controller and evaluate the upper bound of the singular perturbation parameter. Two numerical examples are presented to demonstrate the effectiveness of the proposed design methods.