Stabilisation of descriptor Markovian jump systems with partially unknown transition probabilities. (English) Zbl 1316.93120
Summary: This paper is concerned with the stability and stabilization problems for continuous-time descriptor Markovian jump systems with partially unknown transition probabilities. In terms of a set of coupled Linear Matrix Inequalities (LMIs), a necessary and sufficient condition is firstly proposed, which ensures the systems to be regular, impulse-free and stochastically stable. Moreover, the corresponding necessary and sufficient condition on the existence of a mode-dependent state-feedback controller, which guarantees the closed-loop systems stochastically admissible by employing the LMI technique, is derived; the stabilizing state-feedback gain can also be expressed via solutions of the LMIs. Finally, numerical examples are given to demonstrate the validity of the proposed methods.
MSC:
| 93E15 | Stochastic stability in control theory |
| 60J75 | Jump processes (MSC2010) |
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 93C05 | Linear systems in control theory |
Keywords:
stability and stabilization; descriptor Markovian jump systems; partially unknown transition probabilities; linear matrix inequalitiesReferences:
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