Section: New Results

Time-delay systems

Participants : Jean-Pierre Richard, Jean-Pierre Barbot, Thierry Floquet, Gang Zheng, Denis Efimov, Wilfrid Perruquetti.

• [22] considers a networked control loop, where the plant is a "slave" part, and the remote controller and observer constitute the “master". Since the performance of Networked Control Systems (NCS) depends on the Quality of Service (QoS) available from the network, it is worth to design a controller that takes into account qualitative information on the QoS in realtime. The goal of the design is to provide a controller that guarantees two things: 1) high performances (here expressed by exponential decay rates) when the QoS remains globally the same; 2) global stability when the QoS changes. In order to guarantee the global stability, the controller will switch by respecting a dwell time constraint. The dwell time parameters are obtained by using the switched system theories and the obtained conditions are Linear Matrix Inequalities (LMI).

• Causal and non-causal observabilities are discussed in [33] for nonlinear time-delay systems with unknown inputs. Using the theory of non-commutative rings and the algebraic framework, the nonlinear time-delay system is transformed into a suitable canonical form to solve the problem. A necessary and sufficient condition is given to guarantee the existence of a change of coordinates leading to such a form.

• The notion of homogeneity is extended to the time-delay nonlinear systems in [45] . It is shown that under some conditions the stability of homogeneous functional systems on a sphere implies the global stability of the system. The notion of local homogeneity is introduced, the relations between stability of the locally approximating dynamics and the original time-delay system are established.

• [38] addresses the problem of the position/force tracking in tele-operation system and proposes a haptic proxy control scheme, in which communication delays are assumed to be both time-varying and asymmetric, and the response of the synchronization and the transparency are improved. The control design is performed using Linear Matrix Inequality (LMI) optimization based on Lyapunov-Krasovskii functionals (LKF) and H${}_1$ control theory.

• Stability and synchronization of systems with time-varying delays is studied in [37] , in which a novel control scheme with position/velocity information channel on the basis of Lyapunov-Krasovskii functional (LKF) and H${}_1$ control theory by using Linear Matrix Inequality (LMI) is proposed. The proposed solution is efficient for different working conditions, such as abrupt motion and wall contact illustrated by various simulations.

• Embedded systems can benefit from all results on variable sampling for delayed systems [18] , [19] and [47] .