New approach to H∞ control for Markovian jump singular systems

This study investigates the H_∞ control problem for a class of continuous-time Markovian jump singular systems. The authors´ attention is focused on the design of state and static output feedback controllers which ensure that the closed-loop system is regular, impulse-free and stochastically stable, and satisfies a prescribed H_∞ performance level. To investigate the problem of H_∞ performance analysis for the system under consideration, a bounded real lemma (BRL) is provided in terms of linear matrix inequality (LMI) containing equality constraints, which may not be a problem from the theoretical point of view, but may cause great big trouble in checking the conditions numerically. To solve this problem, a new version of BRL is also provided in terms of strict LMIs. Based on this, two approaches are established to solve the problem of state feedback H_∞ control, and then, the problem of static output feedback H_∞ control is solved, which can also be used for solving the dynamic output feedback control problems. Finally, two numerical examples are given to illustrate the effectiveness of the obtained theoretical results.