Réunions du groupe

1 février 2012

Paris, LSS

GdRE DELSYS

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09h30-09H45:     Welcome

09h45-10h15:     Yan, X., “Decentralised output feedback sliding mode control for interconnected time delay systems”

In this paper, global decentralised stabilisation of a class of interconnected time-varying delay systems is considered, where both known and uncertain interconnections involve time delay. Matched and mismatched interconnections are considered separately to reduce the conservatism. A composite sliding surface is designed and the stability of the associated sliding motion, which is governed by a time delayed interconnected system, is analysed based on the Razumikhin-Lyapunov approach. The attractive features of sliding mode techniques and the system structure are fully exploited. A decentralised static output feedback variable structure control which is dependent on time-delay is synthesized to drive the interconnected system to the sliding surface globally. Simulation results show the effectiveness of the proposed approach.

10h15-10h30:    Coffee Break

10h30-11h15:     Seuret, A., “A novel stability analysis of linear systems under asynchronous samplings'

This presentation proposes a novel approach to assess stability of continuous linear systems with sampled-data inputs. The method, which is based on the discrete-time Lyapunov theorem, provides easy tractable stability conditions for the continuous-time model. Sufficient conditions for asymptotic and exponential stability are provided dealing with synchronous and asynchronous samplings and uncertain systems. An additional stability analysis is provided for the cases of multiple sampling periods and packet losses. Several examples show the efficiency of the method.

11h15-12h00:    Olaru, S. : On Positive Invariance for Delay Difference Equations

In this talk we recall several polyhedral concepts related to the control of time delay systems covering: the modeling in terms of polytopic uncertainties, the invariance analysis, the constraints satisfaction, the constrained control design.
As an important contribution we introduce a new concept of set invariance, called D-invariance for discrete time-delay systems. More specifically we are interested in the definition and computation of a D-invariant set with respect to a bounded subset of the state-space. Firstly the D-invariance conditions of polyhedral sets for discrete time-delay systems are derived. Then, by using these conditions, the stabilization problem is proposed in order to obtain a D-invariant state feedback control law. Finally an algorithm is proposed to obtain a D-invariant set for a given dynamics.

12h00-14h00:    Lunch

14h00-14h45:    Rodrigues de Campos, G., and Seuret, A.: “Improved Consensus Algorithms using Memory Effects”

This presentation deals with simple integrator consensus problems. It is well-known that introducing a delay leads in general to a reduction of performances or to instability. Therefore, investigating the effect of time-delays in consensus problems is an important issue. The objective is the design of a improved consensus algorithm for continuous-time multi-agent systems. The novel algorithm proposes to sampled, in an appropriate manner, part of the multi-agent systems information such that the algorithm converges, assuming that at each instant, agent’s control laws will also consider the sampled past information of its neighbors. Stability conditions expressed in terms of LMI’s and based on algebraic communication matrix structure are provided. The efficiency of the method is tested for different network communication schemes.

14h45-15h30:    Ozbay, H., “Stability Analysis of a Distributed Delay System Modeling Cell Dynamics in Leukemia”

In this talk we will discuss stability conditions for cell dynamics in leukemia. Basic biological principles behind the mathematical model will be summarized. The overall system is a cascade connection of sub-systems consisting of distributed delays and static nonlinear feedbacks. We will first present the conditions for local asymptotic stability around the positive equilibrium. For the nonlinear system, we derive stability conditions by using Popov, circle and nonlinear small gain criteria. The results are illustrated with numerical examples and simulations.

15h30-16h15:    Boussaada, I., and Niculescu, S.-I. “Avoiding a triple zero eigenvalue singularity for an inverted pendulum via Multiple Delays”

In this talk we consider a friction free inverted pendulum model. We show that using multiple delayed proportional gains we arrive to avoid the configuration of triple zero eigenvalue. This study is based on the Banach space decomposition Theorem and the center Manifold Theorem.

16h15-16h45:    Discussions