Finite-time stability and asynchronous \(H_\infty\) control for highly nonlinear hybrid stochastic systems. (English) Zbl 1533.93710
Summary: In this paper, the \(\mathbf{p}\)th moment finite-time stochastic stability (\(\mathbf{p}\)-MFTS stability) and asynchronous \(H_\infty\) control for highly nonlinear hybrid stochastic systems (HNHSSs) are investigated. Firstly, the definition of \(\mathbf{p}\)-MSFT stability for HNHSSs is proposed, and the stability criteria are given by the mode-dependent average dwell time (MDADT) method. Secondly, the asynchronous \(H_\infty\) controller is designed to ensure that HNHSSs are \(\mathbf{p}\)th moment finite-time stochastically stabilizable (\(\mathbf{p}\)-MFTS stabilizable) and satisfy \(H_\infty\) performance. When designing the asynchronous \(H_\infty\) controller, deterministic asynchrony and stochastic asynchrony are considered simultaneously. Moreover, since the coefficients of HNHSSs have highly nonlinear structures without satisfying the linear growth condition (LGC), the Lyapunov function \(\mathcal{U}\) and the operator \(L\mathcal{U}\) are bounded by polynomials of degree higher than \(\mathbf{p}\), which means that weaker conditions of \(\mathbf{p}\)-MFTS stability are proposed. Finally, examples are presented to illustrate the availability of the results.
MSC:
| 93D40 | Finite-time stability |
| 93E15 | Stochastic stability in control theory |
| 93B36 | \(H^\infty\)-control |
| 93C10 | Nonlinear systems in control theory |
| 93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |
Keywords:
highly nonlinear stochastic systems; \(\mathbf{p}\)th moment finite-time stability; asynchronous \(H_\infty\) control; Markov process; deterministic switchingReferences:
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