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Lhachemi, Hugo
Preferred name
Lhachemi, Hugo
Official Name
Lhachemi, Hugo
Research Output
Now showing 1 - 3 of 3
- PublicationRobustness of constant-delay predictor feedback for in-domain stabilization of reaction–diffusion PDEs with time- and spatially-varying input delaysThis paper discusses the in-domain feedback stabilization of reaction–diffusion PDEs with Robin boundary conditions in the presence of an uncertain time- and spatially-varying delay in the distributed actuation. The proposed control design strategy consists of a constant-delay predictor feedback designed based on the known nominal value of the control input delay and is synthesized on a finite-dimensional truncated model capturing the unstable modes of the original infinite-dimensional system. By using a small-gain argument, we show that the resulting closed-loop system is exponentially stable provided that the variations of the delay around its nominal value are small enough. The proposed proof actually applies to any distributed-parameter system associated with an unbounded operator that 1) generates a -semigroup on a weighted space of square integrable functions over a compact interval; and 2) is self-adjoint with compact resolvent.
148Scopus© Citations 15 - PublicationControl Law Realification for the Feedback Stabilization of a Class of Diagonal Infinite-Dimensional Systems With Delay Boundary ControlRecently, a predictor feedback control strategy has been reported for the feedback stabilization of a class of infinite-dimensional Riesz-spectral boundary control systems exhibiting a finite number of unstable modes by means of a delay boundary control. Nevertheless, for real abstract boundary control systems exhibiting eigenstructures defined over the complex field, the direct application of such a control strategy requires the embedding of the control problem into a complexified state-space which yields a complex-valued control law. This letter discusses the realification of the control law, i.e., the modification of the design procedure for obtaining a real-valued control law for the original real abstract boundary control system. The obtained results are applied to the feedback stabilization of an unstable Euler-Bernoulli beam by means of a delay boundary control.
166Scopus© Citations 9 - PublicationAn LMI condition for the robustness of constant-delay linear predictor feedback with respect to uncertain time-varying input delaysThis paper discusses the robustness of the constant-delay predictor feedback in the case of an uncertain time-varying input delay. Specifically, we study the stability of the closed-loop system when the predictor feedback is designed based on the knowledge of the nominal value of the time-varying delay. By resorting to an adequate Lyapunov–Krasovskii functional, we derive an LMI-based sufficient condition ensuring the exponential stability of the closed-loop system for small enough variations of the time-varying delay around its nominal value. These results are extended to the feedback stabilization of a class of diagonal infinite-dimensional boundary control systems in the presence of a time-varying delay in the boundary control input.
162Scopus© Citations 33