Convex dwell-time characterizations for uncertain linear impulsive systems

New sufficient conditions for the characterization of dwell-times for linear impulsive systems are proposed and shown to coincide with continuous decrease conditions of a certain class of looped-functionals, a recently introduced type of functionals suitable for the analysis of hybrid systems. This approach allows to consider Lyapunov functions that evolve non-monotonically along the flow of the system in a new way, broadening then the admissible class of systems which may be analyzed. As a byproduct, the particular structure of the obtained conditions makes the method is easily extendable to uncertain systems by exploiting some convexity properties. Several examples illustrate the approach.Comment: Accepted at IEEE Transactions on Automatic Contro

Time-triggered and event-triggered control of switched affine systems via a hybrid dynamical approach

This paper focuses on the design of both periodic time- and event-triggered control laws of switched affine systems using a hybrid dynamical system approach. The novelties of this paper rely on the hybrid dynamical representation of this class of systems and on a free-matrix min-projection control, which relaxes the structure of the usual Lyapunov matrix-based min-projection control. This contribution also presents an extension of the usual periodic time-triggered implementation to the event-triggered one, where the control input updates are permitted only when a particular event is detected. Together with the definition of an appropriate optimization problem, a stabilization result is formulated to ensure the uniform global asymptotic stability of an attractor for both types of controllers, which is a neighborhood of the desired operating point. Finally, the proposed method is evaluated through a numerical example.Agence Nationale de la Recherche (ANR)France Grant ANR-18-CE40-0022-01Agencia Estatal de Investigación (AEI)-Spain Grant PID2019-105890RJ-10

Control of a remote system over network including delays and packet dropout

International audienceThis work concerns the observer-based control of a remote, Master-Slave system through the Internet network. This communication link introduces variable, asymmetric and unpredictable delays, as well as packet loss. The data-sampling effects are also taken into account, even in the aperiodic case. Whereas the existing strategies require additional buffers, allowing the delay to become constant, the present result uses the information as soon as received. The proposed Lyapunov-Krasovskii functionals and LMI algorithms provide controller and observer gains which ensure the asymptotic stability of the global closed loop. The maximum admissible number of successive packets dropouts is also computed. The last part of the paper provides a simulation, where the Slave is a second-order system

On the necessity of sufficient LMI conditions for time-delay systems arising from Legendre approximation

This work is dedicated to the stability analysis of time-delay systems with a single constant delay using the Lyapunov-Krasovskii theorem. This approach has been widely used in the literature and numerous sufficient conditions of stability have been proposed and expressed as linear matrix inequalities (LMI). The main criticism of the method that is often pointed out is that these LMI conditions are only sufficient, and there is a lack of information regarding the reduction of the conservatism. Recently, scalable methods have been investigated using Bessel-Legendre inequality or orthogonal polynomial-based inequalities. The interest of these methods relies on their hierarchical structure with a guarantee of reduction of the level of conservatism. However, the convergence is still an open question that will be answered for the first time in this paper. The objective is to prove that the stability of a time-delay system implies the feasibility of these scalable LMI, at a sufficiently large order of the Legendre polynomials. Moreover, the proposed contribution is even able to provide an analytic estimation of this order, giving rise to a necessary and sufficient LMI for the stability of time-delay systems

Exponential Stabilization of Delay Neutral Systems under Sampled-Data Control

International audienceThis paper considers the exponential stabilization of delay systems of the neutral type via sampled-data control. The control input of the neutral system can present a delay, constant or variable. The sampling period is not necessarily constant. It is only assumed that the time between to successive sampling instants is bounded. Since the sampling effect (sampling and zero-holder) is equivalent to a variable delay, the resulting system is modelled as a continuous-time one, where the control input has a ‘non-small' time-varying delay belonging to some interval [h−μ,h+μ]. For instance, h−μ may represent the minimum input delay, and 2μ the additional delay generated by the combination of the sampling effect with the input delay variation. This results in a system with ‘nonsmall' time-varying delays (i.e. delays with a known and nonzero minimum value), the exponential stabilization of which is possible under LMI conditions. Two examples are provided. The first one deals with the sampled-data control of a neutral system. The second one considers the stabilization of a flexible rod with continuous, delayed control

Robust sampled-data control: An input delay approach

International audienceA method for robust sampled-data stabilization of linear continuous-time systems is introduced. This method is based on the continuous-time model with time-varying input delay. Delay-dependent sufficient LMIs conditions for stabilization of systems with polytopic type uncertainty and for regional stabilization of systems with sampled-data saturated state-feedback are derived. The method may be applied to a wide spectrum of robust sampled-data control problems

A looped-functional approach for robust stability analysis of linear impulsive systems

A new functional-based approach is developed for the stability analysis of linear impulsive systems. The new method, which introduces looped-functionals, considers non-monotonic Lyapunov functions and leads to LMIs conditions devoid of exponential terms. This allows one to easily formulate dwell-times results, for both certain and uncertain systems. It is also shown that this approach may be applied to a wider class of impulsive systems than existing methods. Some examples, notably on sampled-data systems, illustrate the efficiency of the approach.Comment: 13 pages, 2 figures, Accepted at Systems & Control Letter

Design of a pressure control system with dead band and time delay

This paper investigates the control of pressure in a hydraulic circuit containing a dead band and a time varying delay. The dead band is considered as a linear term and a perturbation. A sliding mode controller is designed. Stability conditions are established by making use of Lyapunov Krasovskii functionals, non-perfect time delay estimation is studied and a condition for the effect of uncertainties on the dead zone on stability is derived. Also the effect of different LMI formulations on conservativeness is studied. The control law is tested in practice

Stability Criteria for Asynchronous Sampled-data Systems - A Fragmentation Approach

International audienceThe stability analysis of asynchronous sampled-data systems is studied. The approach is based on a recent result which allows to study, in an equivalent way, the quadratic stability of asynchronous sampled-data systems in a continuous-time framework via the use of peculiar functionals satisfying a necessary boundary condition. The method developed here is an extension of previous results using a fragmentation technique inspired from recent advances in time-delay systems theory. The approach leads to a tractable convex feasibility problem involving a small number of finite dimensional LMIs. The approach is then finally illustrated through several examples