Distributed sampled-data control of Kuramoto-Sivashinsky equation. (English) Zbl 1402.93172
Summary: The paper is devoted to distributed sampled-data control of nonlinear PDE system governed by 1-D Kuramoto-Sivashinsky equation. It is assumed that \(N\) sensors provide sampled in time spatially distributed (either point or averaged) measurements of the state over \(N\) sampling spatial intervals. Locally stabilizing sampled-data controllers are designed that are applied through distributed in space shape functions and zero-order hold devices. Given upper bounds on the sampling intervals in time and in space, sufficient conditions ensuring regional exponential stability of the closed-loop system are established in terms of Linear Matrix Inequalities (LMIs) by using the time-delay approach to sampled-data control and Lyapunov-Krasovskii method. As it happened in the case of diffusion equation, the descriptor method appeared to be an efficient tool for the stability analysis of the sampled-data Kuramoto-Sivashinsky equation. An estimate on the domain of attraction is also given. A numerical example demonstrates the efficiency of the results.
MSC:
| 93C57 | Sampled-data control/observation systems |
| 93C10 | Nonlinear systems in control theory |
| 93C20 | Control/observation systems governed by partial differential equations |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
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