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Abstract

In this paper, the problem of practical stabilization of linear time-varying continuous systems is considered. Necessary and sufficient conditions, based upon the solution to some Lyapunov differential matrix equations, are proposed for particular cases of interest. From these conditions, the design of time-varying state feedback controller guaranteeing the finite time closed-loop stability is presented. Numerical experiments illustrate the potentialities of the approach.

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Abstract

This paper presents a systematic approach for nonlinear control design by using the gain scheduling technique to insure the transition of a nonlinear dynamical process from an actual operating condition to a desired one. The nonlinear system is represented in neighborhoods of equilibrium points by a family of polytopic uncertain linear systems. The nonlinear equations of the system are imbedded in the interior of an inclusion polyhedron. A robust control law is built so as to insure asymptotic stability to a given equilibrium within a maximal ellipsoidal region contained in the interior of the polyhedron. Given a pre-specified equilibrium curve connecting the initial and final points, it is shown how to fix a sequence of equilibrium points together with the local associated ellipsoids covering the curve and enabling a convergent control sequence. State feedback and output feedback for the local robust control synthesis are considered, together with local performance criteria. A simple numerical experiment is provided to illustrate both the effectiveness of the synthesis and the performance achieved.

Abstract

This paper addresses the problem of controlling linear systems with both sensors and actuators subject to saturation. Supposing that only the output of the linear plant is measurable, the synthesis of stabilizing output feedback dynamic controllers is considered. It is shown that, in this case, the closed-loop system presents a nested saturation term. Therefore, based on the use of some generalized sector conditions and appropriate variable changes, synthesis conditions in a "quasi"-LMI form are stated in both regional (local) as well as global contexts. Concerning the regional results, an LMI-based optimization problem for computing a controller in order to enlarge the region of attraction of the closed-loop system is proposed.

Abstract

Necessary and sufficient conditions for the existence and design of disturbance decoupled reduced-order observers for continuous linear descriptor systems are presented. The observer existence conditions are based on the solution of a generalized Sylvester's equation, under a constraint that describes the disturbance decoupling of the estimated state, and on a rank condition that guarantees the existence of matrices for the reconstruction of all state variables, also with disturbance decoupling. Basically, the design conditions of the desired observer are associated to some structural properties of the descriptor system. From these results, we propose an observer design algorithm that is based on eigenstructure assignment technique. The presented results are useful when an estimated state feedback control law is considered. An illustrative numerical example is reported.

Mots-Clés / Keywords