Robust stabilisation of discrete-time time-varying linear systems with Markovian switching and nonlinear parametric uncertainties. (English) Zbl 1290.93154
Summary: In this paper, the problem of the robustness of the stability of a discrete-time linear stochastic system is addressed. The nominal plant is described by a discrete-time time-varying linear system subject to random jumping according with a non-homogeneous Markov chain with a finite number of states. The class of admissible uncertainties consists of multiplicative white noise type perturbations with unknown intensity. It is assumed that the intensity of white noise type perturbations is modeled by unknown nonlinear functions subject to linear growth conditions. The class of admissible controls consists of stabilizing state feedback control laws. We show that the best robustness performance is achieved by the stability provided by a state feedback design based on the stabilizing solution of a suitable discrete-time Riccati-type equation.
MSC:
| 93D21 | Adaptive or robust stabilization |
| 93E15 | Stochastic stability in control theory |
| 93C55 | Discrete-time control/observation systems |
| 60J75 | Jump processes (MSC2010) |
| 93C41 | Control/observation systems with incomplete information |
| 60H40 | White noise theory |
Keywords:
robust stability and robust stabilization; nonlinear parametric uncertainties; discrete-time stochastic systems; non-homogeneous Markov chains; discrete-time Riccati-type equationsReferences:
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