A global high-gain finite-time observer

International audienceA global finite-time observer is designed for nonlinear systems which are uniformly observable and globally Lipschitz. This result is based on a high-gain approach combined with recent advances on finite-time stability using Lyapunov function and homogeneity concepts

Resilient Observer Design for Discrete-Time Nonlinear Systems with General Criteria

A class of discrete-time nonlinear system and measurement equations having incrementally conic nonlinearities and finite energy disturbances is considered. A linear matrix inequality based resilient observer design approach is presented to guarantee the satisfaction of a variety of performance criteria ranging from simple estimation error boundedness to dissipativity in the presence of bounded perturbations on the gain. Some simulation examples are included to illustrate the proposed design methodology

On dynamical feedback control design for generalized homogeneous differential inclusions

International audienceIn the present paper, the stability criterion for generalized homogeneous differential inclusions is obtained that may simplify the control design procedure in some particular cases. Robust dynamical feedback control law is designed for homogeneous differential inclusions. Performance of the resulting dynamical feedback is illustrated by numerical simulation

Finite-time Stabilization Using Implicit Lyapunov Function Technique

International audienceThe Implicit Lyapunov Function (ILF) method for finite-time stability analysis is introduced. The control algorithm for finite-time stabilization of a chain of integrators is developed. The scheme of control parameters selection is presented by a Linear Matrix Inequality (LMI). The robustness of the finite-time control algorithm with respect to system uncertainties and disturbances is studied. The new high order sliding mode (HOSM) control is derived as a particular case of the developed finite-time control algorithm. The settling time estimate is obtained using ILF method. The algorithm of practical implementation of the ILF control scheme is discussed. The theoretical results are supported by numerical simulations

Observation of Nonlinear Differential-Algebraic Systems with Unknown Inputs

International audienceA method to carried out the state estimation is proposed for a class of nonlinear systems with unknown inputs whose dynamics is governed by differential-algebraic equations (DAE). We achieve, under suitable conditions, to replace the original DAE for a system with differential equations only by using a zeroing manifold algorithm inducing a state space dimension reduction. Observability conditions can be checked using the original system parameters. The state estimation is done using a sliding mode high order differentiator

A high-gain-based global finite-time nonlinear observer

In this paper, a global finite-time observer is designed for a class of nonlinear systems with bounded rational powers imposed on the incremental nonlinearities. Compared with the previous global finite-time results, the new observer designed here is with a new gain update law. Moreover, an example is given to show that the proposed observer can reduce the time of the observation error convergence.National Science Foundation of China (Nos. 61074091, 61174216 and 51177088), the National Science Foundation of Hubei Province (2010CDB10807, 2011CDB187) and the Scientific Innovation Team Project of Hubei Provincial Department of Education (T200809, T201103).http://www.tandfonline.com/loi/tcon20hb201

Robust finite-time output feedback stabilization of the double integrator

International audienceThe problem of finite-time output stabilization of the double integrator is addressed applying the homogeneity approach. A homogeneous controller and a homogeneous observer are designed (for different degrees of homogeneity) ensuring the finite-time stabilization. Their combination under mild conditions is shown to stay homogeneous and finite-time stable as well. Robustness and effects of discretization on the obtained closed loop system are analyzed. The efficiency of the obtained solution is demonstrated in computer simulations

Stabilité et stabilisation en temps fini des systèmes dynamiques interconnectés et problème de consensus en temps fini

This manuscript is dedicated to the study of finite time stability and stabilization of interconnected dynamical systems and finite time consensus problem. After a general introduction, the first part of this thesis focuses on finite time stability and stabilization of perturbed systems and interconnected systems. The second part of this thesis is devoted to the problems of: finite-time consensus, average consensus and finite time stabilization of multi-agent systems. This concept has been addressed by targeting non-linear controlled dynamical systems: with and without drift term. Some protocols are proposed to solve the finite time consensus problem. Many applications and simulations are illustrated.Ce manuscrit est dédié à l'étude de la stabilité et la stabilisation en temps fini des systèmes dynamiques interconnectés et problème de consensus en temps fini. Après une large introduction, la première partie de ce mémoire se focalise sur la stabilité et stabilisation en temps fini des systèmes dynamiques perturbés et des systèmes dynamiques interconnectés. La deuxième partie de cette thèse est consacrée aux problèmes de : consensus en temps fini, consensus moyen en temps fini et stabilisation en temps fini des systèmes multi-agents. Cette notion a été abordé en ciblant les systèmes dynamiques contrôlés non linéaires et complexes de type avec et sans terme de dérive et affine en la commande. Des protocoles sont mis en exergue résolvant les problèmes de consensus/formation en temps fini entre les états de tels systèmes. De nombreuses applications avec des simulations permettent de confirmer les protocoles proposés

Corrections to "A Global High-Gain Finite-Time Observer"

International audienceThis note fixes the proof of Theorem 2 in the above paper