Abstract
The aim of this manuscript is to tackle the tracking problem for uncertain semi-Markov systems. More precisely, the mode-dependent event-triggering communication approach is introduced for networked controller design procedure, which can considerably increase the signal transmission efficiency. Based on the Lyapunov–Krasovski method, mode-dependent sufficient conditions are derived and the tracking errors could achieve the asymptotic mean-square stability, and mode-dependent controllers could be further calculated by convex optimization. A numerical simulation with application to vertical take-off and landing helicopter would be performed for verifying the availability and usefulness.
Highlights
Markov jump systems (MJSs) have drawn a lot of research attention owing to their ability for modeling practical systems with jumping parameters governed by a Markov chain.[1,2,3,4,5]
It is worth mentioning that often transition probability may be not kept constant in certain scenario, we formulated the semi-Markovian jump systems (SMJSs).[9]
Some initial efforts have been paid to SMJS with remarkable methods including stability problem,[10] state estimation problem,[11] and synchronization problem.[12]
Summary
Markov jump systems (MJSs) have drawn a lot of research attention owing to their ability for modeling practical systems with jumping parameters governed by a Markov chain.[1,2,3,4,5] To name a few, power systems,[6] neural systems,[7] robotic systems[8] can be effectively described by MJSs with corresponding analysis and synthesis results. Remarkable results can be found,[24,25] where effective event-triggered control strategies have been developed. To the best of the authors’ knowledge, the challenging and open problems for the tracking control problem of SMJS with effective event-triggered mechanism still exists, especially with the modedependent strategies. Inspired by the what have been discussed above, the tracking problem of SMJS accompied by modedependent parameter uncertainties is studied by proposing a mode-dependent event-triggered transmission scheme. To this end, the aim of our manuscript is going to project a desired mode-dependent controller for ensuring the H‘-tracking performance, and the following lemmas are provided for deriving the main results. F T(t)F (t)4I.30 L + HF E + ETF THT 0 0, if and only if there exists a scalar e . 0 such that
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