Michael Di Loreto

Exponential L 2 -stability for a class of linear systems governed by continuous-time difference equations

Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate L 2 -stability for such a class of systems. Sufficient conditions, and in some particular cases, necessary and sufficient conditions for exponential L 2 -stability are established, for multivariable systems with commensurate or rationally independent delays. An analysis of discontinuities evolution appearing in the system response is proposed. Finally, a robustness issue is discussed for time-varying delays.

On the role of essential orders on feedback decoupling and model inversion : bond graph approach

The essential orders have an important role in the study of the systems decouplability as well as in the inverse model characterization. The aim of this paper is first to define essential orders on the bond graph model. Secondly, static and dynamic decoupling by bond graph approach is discussed and the dynamic extension order is defined. Finally, the dynamic compensation is physically located on the bond graph model and an approach to synthesize a model statically decouplable is suggested in order to define an adequate structure to the control requirements.

Hamiltonian systems discrete-time approximation: Losslessness, passivity and composability

Abstract In this paper a passive integrator dedicated to input/output Hamiltonian systems approximation is presented. In a first step, a discrete Hamiltonian framework endowed with a Lie derivative-like formula is introduced. It is shown that the discrete dynamics encodes energy conservation and passivity. Additionally, the characterization of the discrete dynamics in terms of Dirac structure is shown to be invariant by interconnection. The class is thus composable: networked systems belong to the class. In a second step, the discrete dynamics is considered as a one-step integration method. The method is shown to be convergent and provides a discrete-time approximation of an input/output Hamiltonian system. Accordingly, the discrete dynamics inherits intrinsic energetic characteristics (storage function and dissipation rate) from the original system. The method is thus tagged as passive integrator. As an illustration, the closed-loop behavior of interconnected subsystems and the stabilization of a rigid body spinning around its center of mass are presented.

A periodic approach for input-delay problems: Application to network controlled systems affected by polytopic uncertainties

This paper deals with robust stability and stabilization of linear discrete-time systems subject to uncertainties and network constraints. In network control systems, the control loop is closed over a network, which induces additional dynamics to the original control loop such as delays, sampling, quantization among many others. This paper focuses on networked induced delays due to unreliable network for which packet losses may occur. An equivalent periodic-like representation of the resulting system is proposed. This allows first, to revisit existing results in this framework and second, to take model uncertainties into account by analyzing the closed-loop model by means of a recent method based on robust control for discrete-time time-varying systems. Stability analysis and dynamic state-feedback stabilization are characterized via new conditions, whose conservatism is extensively discussed. Effectiveness of the proposed methodology is illustrated by numerical examples.

Stability and Stabilization for Continuous-Time Difference Equations with Distributed Delay

Motivated by linear hyperbolic conservation laws , we investigate in this chapter new conditions for stability and stabilization for linear continuous-time difference equations with distributed delay . For this, we propose first a state-space realization of networks of linear hyperbolic conservation laws via continuous-time difference equations. Then, based on some recent works, we propose sufficient conditions for exponential stability , which appear also to be necessary and sufficient in some particular cases. Then, the stabilization problem as well as the closed-loop performances are analyzed with constructive methods for state feedback synthesis.

Approximation of linear distributed parameter systems by delay systems

The present work addresses continuous-time approximation of distributed parameter systems governed by linear one-dimensional partial differential equations. While approximation is usually realized by lumped systems, that is finite dimensional systems, we propose to approximate the plant by a time-delay system. Within the graph topology, we prove that, if the plant admits a coprime factorization in the algebra of BIBO-stable systems, any linear distributed parameter plant can be approximated by a time-delay system, governed by coupled differential-difference equations. Considerations on stabilization and state-space realization are carried out. A numerical method for constructive approximation is also proposed and illustrated.