Performance evaluation of sampled-data control of Markov jump linear systems. (English) Zbl 1375.93079
Summary: This technical communique extends the recent results of Geromel and Gabriel (2015) to \(\mathcal{H}_\infty\) sampled-data control design of Markov Jump Linear Systems (MJLS). It fulfills a lack of a specific necessary and sufficient result in the literature of sampled-data control of MJLS in the context of \(\mathcal{H}_\infty\) performance. Mean square stabilizability and performance determination are addressed and discussed in a unified theoretical viewpoint. As a natural consequence, it is shown that the previous result of Geromel and Gabriel (2015) is obtained as a particular case. A globally uniformly convergent algorithm is proposed to solve the design conditions. The theory is illustrated by means of an example.
MSC:
| 93C57 | Sampled-data control/observation systems |
| 93E15 | Stochastic stability in control theory |
| 60J75 | Jump processes (MSC2010) |
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 93E20 | Optimal stochastic control |
References:
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