Stochastically exponential stability and stabilization of uncertain linear hyperbolic PDE systems with Markov jumping parameters. (English) Zbl 1244.93167
Summary: This paper is concerned with the problem of robustly stochastically exponential stability and stabilization for a class of distributed parameter systems described by uncertain linear First-Order Hyperbolic Partial Differential Equations (FOHPDEs) with Markov jumping parameters, for which the manipulated input is distributed in space. Based on an Integral-type Stochastic Lyapunov Functional (ISLF), a sufficient condition of robustly stochastically exponential stability with a given decay rate is first derived in terms of Spatial Differential Linear Matrix Inequalities (SDLMIs). Then, an SDLMI approach to the design of robust stabilizing controllers via state feedback is developed from the resulting stability condition. Furthermore, using the finite difference method and the standard Linear Matrix Inequalities (LMIs) optimization techniques, recursive LMI algorithms for solving the SDLMIs in the analysis and synthesis are provided. Finally, a simulation example is given to demonstrate the effectiveness of the developed design method.
MSC:
| 93E12 | Identification in stochastic control theory |
| 93C20 | Control/observation systems governed by partial differential equations |
| 60J75 | Jump processes (MSC2010) |
| 93C05 | Linear systems in control theory |
| 93B35 | Sensitivity (robustness) |
Keywords:
distributed parameter systems; Markov jumping parameters; stochastically exponential stability; robust control; linear matrix inequalities (LMIs)Software:
LMI toolboxReferences:
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