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New approach to H∞ control for Markovian jump singular systems

New approach to H∞ control for Markovian jump singular systems

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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.

Inspec keywords: closed loop systems; control system synthesis; continuous time systems; Markov processes; state feedback; stability; H∞ control; linear matrix inequalities; stochastic systems

Other keywords: control design; bounded real lemma; closed-loop system; continuous-time Markovian jump singular system; H∞ performance level; equality constraint; linear matrix inequality; dynamic output feedback control; state output feedback controller; H∞ control; stochastic stability; static output feedback controller

Subjects: Time-varying control systems; Markov processes; Control system analysis and synthesis methods; Algebra; Stability in control theory; Optimal control

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