The Internal Model Principle:Asymptotic Tracking and Regulation in the Behavioral Framework

Given a plant, together with an exosystem generating the disturbances and the reference signals, the problem of asymptotic tracking and regulation is to find a controller such that the to-be-controlled plant variable tracks the reference signal regardless of the disturbance acting on the system. If a controller achieves this design objective, we call it a regulator for the plant with respect to the given exosystem. In this paper we formulate the asymptotic tracking and regulation problem in the behavioral framework, with control as interconnection. The problem formulation and its resolution are completely representation free, and specified only in terms of the plant and exosystem dynamics

Dissipative Systems Synthesis:a Linear Algebraic Approach

In this paper we consider the problem of synthesis of dissipative systems for the case that first and higher order derivatives of the concerned variables also appear in the weighting function. The problem is formulated and solved using the behavioral approach to systems and control. It turns out that this problem can be reformulated analogously as a problem of finding a non-negative subspace (non-negative with respect to a given indefinite constant symmetric matrix) within a finite dimensional vector space satisfying certain inclusion and dimensionality constraints

Dissipative systems synthesis:A linear algebraic approach

AbstractIn this paper we consider the problem of synthesis of dissipative systems for the case that first and higher order derivatives of the concerned variables also appear in the weighting function. The problem is formulated and solved using the behavioral approach to systems and control. We relate the problem of weighted H∞ control as a special case of this synthesis problem. The synthesis problem and its solution can be systematically understood when one notices that it is similar to finding a non-negative subspace (non-negative with respect to a given constant matrix) within a finite dimensional vector space satisfying certain inclusion and dimension constraints