Jean-Claude Vivalda

On the Convergence of Linear Switched Systems

This paper investigates sufficient conditions for the convergence to zero of the trajectories of linear switched systems. We provide a collection of results that use weak dwell-time, dwell-time, strong dwell-time, permanent and persistent activation hypothesis. The obtained results are shown to be tight by counterexample. Finally, we apply our result to the three-cell converter.

Global Asymptotic Output Feedback Stabilization of Feedforward Systems

The problem of the global asymptotic stabilization by dynamic output feedback of systems belonging to a particular family of feedforward systems is solved. The equations considered depend nonlinearly on the unmeasured part of the state and are nonminimum phase. Feedback laws arbitrarily small in norm are constructed. The result can be applied repeatedly. It is illustrated by the cart-pendulum system with the angle and the position as output.

Stabilization of nonlinear systems: a bilinear approach

This paper gives a necessary and sufficient condition for the stabilization of planar bilinear systems. Local stabilization results are obtained for other systems.

Dynamic output feedback for switched linear systems based on a LQG design

The aim of this paper is to extend the LQG design for linear system to the case of switched linear systems in continuous time. The main result provides a control Lyapunov function and a dynamic output feedback law leading to sub-optimal solutions. Practically, the dynamic output feedback is easy to apply and the design procedure is effective if there exists at least one controllable and observable convex combination of the subsystems. Practical applications concern the large class of power converters.

On the preservation of observability under sampling

Abstract In this paper, we investigate the problem of the preservation of observability under sampling.

Remark on local and global stabilization of homogeneous bilinear systems

In this paper, we deal with the problem of stabilization of homogeneous bilinear systems. The aim is to clarify some results on stabilizability of these systems.

Continuous Discrete Observer with Updated Sampling Period

This paper deals with the design of high gain observers for a class of continuous dynamical systems with discrete-time measurements. Indeed, different approaches based on high gain techniques have been followed in the literature to tackle this problem. Contrary to these works, the measurement sampling time is considered to be variable. Moreover, the new idea of the proposed work is to synthesize an observer requiring the less knowledge as possible from the output measurements. This is done by using an updated sampling time observer. Under the global Lipschitz assumption, the asymptotic convergence of the observation error is established. As an application of this approach, an estimation problem of state of an academic bioprocess is studied, and its simulation results are discussed.

On feedback stabilization of smooth nonlinear systems

This paper deals with the problem of stabilization of nonlinear systems. We present a version of the well-known Jurdjevic-Quinn theorem (1978), concerning affine systems with dissipative drift, for smooth but not necessarily analytic systems. An example and counterexample are proposed.

Self-triggered continuous-discrete observer with updated sampling period

This paper deals with the design of high gain observers for a class of continuous-time dynamical systems with discrete-time measurements. Different approaches based on high gain techniques have been followed in the literature to tackle this problem. Contrary to these works, the measurement sampling time is considered to be variable. Moreover, the new idea of the proposed work is that the use of the output measurements by the observer follows an event based on an extended observer state component. Assuming that the vector fields related to the considered system are globally Lipschitz, the asymptotic convergence of the observation error is established. As an application of this approach, a state estimation problem of an academic bioprocess is studied, and its simulation results are discussed.

An LQ sub-optimal stabilizing feedback law for switched linear systems

The aim of this paper is the design of a stabilizing feedback law for continuous time linear switched system based on the optimization of a quadratic criterion. The main result provides a control Lyapunov function and a feedback switching law leading to sub-optimal solutions. As the Lyapunov function defines a tight upper bound on the value function of the optimization problem, the sub-optimality is guaranteed. Practically, the switching law is easy to apply and the design procedure is effective if there exists at least a controllable convex combination of the subsystems.