REGULATOR PROBLEM FOR LINEAR SYSTEMS WITH CONSTRAINTS ON CONTROL AND ITS INCREMENT Fouad MESQUINE , Fernando TADEO , and Abdellah BENZAOUIA University Cadi Ayyad, Faculty of Sciences Department of Physics, Research unit Constrained Robust Regulation B.P. 2390, Marrakesh Morocco E-mail: mesquine@ucam.ac.ma, benzaouia@ucam.ac.ma Departamento de Ingenieria de Sistemas y Automatica Univesidad de Valladolid, 47005 Valladolid, Spain. E-mail: fernando@autom.uva.es Abstract: This paper discusses the problem of constraints on both control and its increment for linear systems in state space form, in both the continuous and discrete time domains. For autonomous linear systems with constrained increment, necessary and sufficient conditions are derived, such that the evolution of the system respects the incremental constraints. It is also derived a pole placement technique to solve inverse problem, deriving stabilizing state feedback controllers which respect constraints on both control and its increment. An illustrative example shows the application of the method. Copyright c IFAC 2002. Keywords: Keywords: Linear Systems, Constraints, Control, Increment, Positive Invariance, Pole assignment 1. INTRODUCTION Usually, real plants or physical plants are subject to constrained variables. The most frequent constraints are of saturation type, that is, limitations on the magnitude of certain variables. Hence, this topic is of continuing interest and one could cite, not ex- haustively, (Benzaouia, and Burgat, 1988; Benzaouia, and Hmamed, 1993; Benzaouia, and Mesquine, 1994; Blanchini 1990;1999 and the references Therein). Other type of constraints were introduced while con- sidering predictive control (GPC) and practical ap- plications that is incremental constraints (Dion, et al.,1987; Clarke et al. 1987; Warwick, and Clarke, 1988). In fact, for some processes, the rate of variables change is limited within certain bounds. These limits can arise from physical constraints that, if exceeded, could damage the process. From our knowledge, no work has been published on incremental constraints using state space representations. Henceforth, this pa- per investigates the problem of stabilizing linear con- tinuous and discrete time systems with constraints on both control and control increment. Necessary and sufficient conditions of positive invariance for incre- mental domains with respect to autonomous systems are given. Furthermore, a link is done between pole assignment procedure and these conditions to find sta- bilizing controllers by state feedback. 1.1 Notations: If is a vector, denotes its derivative with respect to time in the continuous time case or in the discrete-time case. Further, for a scalar we define and , and then we note that Copyright © 2002 IFAC 15th Triennial World Congress, Barcelona, Spain