Detector-based \(H_\infty\) results for discrete-time Markov jump linear systems with partial observations. (English) Zbl 1387.93148
Summary: This paper features new results on \(H_\infty\) analysis and control of linear systems with Markov jump disturbances, in a scenario of partial observations of the jump process. We consider situations in which the jump process can only be measured through a suitable detector. The approach here is general enough to encompass particular scenarios such as that of perfect information and cluster observations of the Markov jump process. The first main result derived in the paper is a Bounded Real Lemma, which provides a method for the \(H_\infty\) analysis of Markov jump linear systems subject to detector-based partial information, via Linear Matrix Inequalities (LMIs). Besides the interest in its own right, the Bounded Real Lemma makes it possible for us to derive new methods for the design of \(H_\infty\) controllers in the considered scenario of partial observations. The proposed design is nonconservative in the scenario of complete information (thanks to a novel clusterization technique derived in this paper), as well as in the case of Bernoulli jumps. A numerical example, regarding the control of an unmanned aerial vehicle, illustrates the profits of our approach.
MSC:
| 93E03 | Stochastic systems in control theory (general) |
| 60J75 | Jump processes (MSC2010) |
| 93B36 | \(H^\infty\)-control |
| 93B07 | Observability |
| 93C85 | Automated systems (robots, etc.) in control theory |
Keywords:
linear systems; stochastic jump processes; \(H_\infty\) control; partial observations; unmanned aerial vehiclesReferences:
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