Remarks on input-to-state stability of collocated systems with saturated feedback

We investigate input-to-state stability (ISS) of infinite-dimensional collocated control systems subject to saturated feedback. Here, the unsaturated closed loop is dissipative and uniformly globally asymptotically stable. Under an additional assumption on the linear system, we show ISS for the saturated one. We discuss the sharpness of the conditions in light of existing results in the literature.Comment: 12 page

Local stabilization of an unstable parabolic equation via saturated controls

We derive a saturated feedback control, which locally stabilizes a linear reaction-diffusion equation. In contrast to most other works on this topic, we do not assume the Lyapunov stability of the uncontrolled system and consider general unstable systems. Using Lyapunov methods, we provide estimates for the region of attraction for the closed-loop system, given in terms of linear and bilinear matrix inequalities. We show that our results can be used with distributed as well as scalar boundary control, and with different types of saturations. The efficiency of the proposed method is demonstrated by means of numerical simulations

Cone-bounded feedback laws for m-dissipative operators on Hilbert spaces

International audienceThis work studies the influence of some constraints on a stabilizing feedback law. It is considered an abstract nonlinear control system for which we assume that there exists a linear feedback law that makes the origin of the closed-loop system globally asymptotically stable. This controller is then modified via a cone-bounded nonlinearity. A well-posedness and a stability theorems are stated. The first theorem is proved thanks to the Schauder fixed-point theorem, the second one with an infinite-dimensional version of LaSalle's Invariance Principle. These results are illustrated on a linear Korteweg-de Vries equation by some simulations and on a nonlinear heat equation