Systems & Control Letters 44 (2001) 111–117 www.elsevier.com/locate/sysconle Stabilizationofhydraulicsystemsusingapassivityproperty F. Mazenc ∗ , E. Richard INRIA Lorraine, Projet CONGE, ISGMP Bˆ at A, Ile du Saulcy, 57 045 Metz Cedex 01, France Received 30 May 2000; received in revised form 10 March 2001; accepted 1 May 2001 Abstract A design of stabilizing control laws for a hydraulic system is carried out by using passivity properties. Control laws which are bounded in the variables of position and velocity are constructed. Dynamic output feedbacks are determined to deal with the case where the variable of velocity is unmeasured. c  2001 Elsevier Science B.V. All rights reserved. Keywords: Hydraulic system; Passivity; Bounded control 1. Introduction The present work is devoted to the problem of sta- bilizing hydraulic systems. Accurate models of these physical devices are available in the literature: see for example [7–9,16,17]. However, most of the works devoted to the problem of stabilizing these physi- cal devices—which present an industrial challenge— exploitthepropertiesofthelinearapproximationatthe origin of their equations [7–9,16,17] or rely on feed- back linearization techniques [2]. These techniques proceed regardless of the physical properties of the systems and in particular of their stability properties. In other words, by linearizing a system, some terms which do not destabilize the system or even stabilize it may be removed. In consequence, feedback lineariza- tion may result in wasteful and nonrobust controls. Recently, a few works based on signicantly dier- ent approaches have been proposed. * Corresponding author. Tel.: +33-3-87-54-72-68. E-mail addresses: mazenc@loria.fr (F. Mazenc), richard@loria.fr (E. Richard). In [1], a simplied model of hydraulic system, dif- ferent from the one studied in the present paper, is considered. The strategy of control design used in this work borrows ideas from the backstepping technique and from the feedback linearization technique. This approach, appealing from a theoretical point of view, presents a serious drawback from a practical point of view. For the implementation of the control law re- quires the evaluation of successive time derivatives of functions corrupted by noises. The main result in [12] relies on a slight extension of the well-known Jurdjevic–Quinn theorem [3]. It turns out that the expressions of all the control laws obtained that way are independent of one of the state variables: the variable of velocity. Another result of asymptotic stabilization of a hy- draulic system by means of a static state feedback in- dependent of the variable of velocity is proposed in [6, Chapter 5]. The technique of proof of this work re- lies on the singular perturbation theory in combination with an input–output linearization of the equations. However it is well-known that some of the con- trol laws which locally exponentially stabilize the 0167-6911/01/$-see front matter c  2001 Elsevier Science B.V. All rights reserved. PII:S0167-6911(01)00130-X