This paper deals with the problem of stability and stabilization of sampled-data systems under asynchronous samplings and actuators saturation. The method is based, on the first hand, on the use of a novel class of Lyapunov functionals whose derivative is negative along the trajectories of the continuoustime model of the sampled data system. It is shown that this fact guarantees that a quadratic Lyapunov function is strictly decreasing for the discrete-time asynchronous system. On the other side, the control saturation is taken into account from the use of a modified sector condition. These ingredients lead to the formulation of improved LMI conditions that can be cast in optimization problems aiming at enlarging estimates of the region of attraction of the closed-loop system or maximizing the bounds on the sampling period jitter for which stability and stabilization are ensured.

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International audienceThis paper deals with a wave equation with a one-dimensional space variable, which describes the dynamics of string deflection. Two kinds of control are considered: a distributed action and a boundary control. It is supposed that the control signal is subject to a cone-bounded nonlinearity. This kind of feedback laws includes (but is not restricted to) saturating inputs. By closing the loop with such a nonlinear control, it is thus obtained a nonlinear partial differential equation, which is the generalization of the classical 1D wave equation. The well-posedness is proven by using nonlinear semigroups techniques. Considering a sector condition to tackle the control nonlinearity and assuming that a tuning parameter has a suitable sign, the asymptotic stability of the closed-loop system is proven by Lyapunov techniques. Some numerical simulations illustrate the asymptotic stability of the closed-loop nonlinear partial differential equations

International audienceThe paper deals with an observer-based event-triggered control strategy for linear systems using only local (that is available) variables. Sufficient conditions based on linear matrix inequalities (LMI) associated to convex optimization problems are proposed to ensure the asymptotic stability of the closed loop and the output convergence to a constant reference in both emulation and co-design contexts. Indeed, the proposed approach allows either to design the event-triggering rules or co-design the event-triggering rule along with the controller gain

This work proposes a new approach to asses stability of sampled-data controlled linear systems under aperiodic sampling and subject to input saturation. From an impulsive representation of the system and considering a partition of the interval between two successive sampling instants, it is shown that the discrete-time dynamics of the closed-loop system can be described by a difference inclusion. A general Lyapunovbased result allowing to conclude about the local stability of the sampled-data system is derived. Thus, considering the particular case of quadratic functions, a constructive condition in terms of linear matrix inequalities (LMIs) is proposed to compute estimates of the region of attraction of the nonlinear closed-loop system.