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We consider and we study a general concept of domination for controlled and observed distributed systems. We give characterization results and the main properties of this notion for controlled systems, with respect to an output operator. We also examine the case of actuators and sensors. Various other situations are considered and applications are given. Then, we extend this study by comparing observed systems with respect to a control operator. Finally, we study the relationship between the notion of domination and the compensation one, in the exact and weak cases.

In this work, we introduce and examine the notion of domination for a class of linear distributed systems. This consists in studying the possibility to make a comparison between input or output operators. We give the main algebraic properties of such relations, as well as characterizations of exact and weak domination. We also study the case of actuators, and various situations are examined. Applications and illustrative examples are also given. By duality, we extend this study to observed systems. We obtain similar results and properties, and the case of sensors is equally examined.

Abstract. This work concerns an enlarged analysis of the problem of asymptotic compensation for a class of discrete linear distributed systems. We study the possibility of asymptotic compensation of a disturbance by bringing asymptotically the observation in a given tolerance zone C. Under convenient hypothesis, we show the existence and the unicity of the optimal control ensuring this compensation and we give its characterization.

Abstract. The domination is an original way for systems classification, based on input and output operators. In this paper, we consider first a class of controlled discrete distributed parameter systems (DPS). We extend the domination concept to these systems. By duality, we consider a classification for discrete observed systems, based on output operators. We give various characterizations and the main properties in the general case, and then by means of the choice of actuators and sensors.