The robust regulation problem with robust stability

Among the most common purposes of control are the tracking of reference signals and the rejection of disturbance signals in the face of uncertainties. The related design problem is called the `robust regulation problem'. Here we investigate the trade-off between the robust regulation constraint and the requirement of robust stability. We first formulate the robust regulation problem as an interpolation problem, and derive from this a number of simple necessary conditions for the robust regulation problem to be solvable with a given stability margin. Then we show that these conditions are also sufficient provided the given stability margin is achievable at all

Regulation as an Interpolation Problem

AbstractThe design of a controller such that the closed-loop system will track reference signals or reject disturbance signals from a specified class is known as the “servomechanism problem” or the “regulator problem.” We show here that the regulator problem can be looked at as an interpolation problem for a subspace-valued function that can be viewed as a multivariable version of the Nyquist curve. The result is applied to obtain a simple parametrization of all solutions

From Lipschitzian to non-Lipschitzian characteristics : continuity of behaviors

Linear complementarity systems are used to model discontinuous dynamical systems such as networks with ideal diodes and mechanical systems with unilateral constraints. In these systems mode changes are modeled by a relation between nonnegative, complementarity variables. We consider approximating systems obtained by replacing this non-Lipschitzian relation with a Lipschitzian function and investigate the convergence of the solutions of the approximating system to those of the ideal system as the Lipschitzian characteristic approaches to the (non-Lipschitzian) complementarity relation. It is shown that this kind of convergence holds for linear passive complementarity systems for which solutions are known to exist and to be unique. Moreover, this result is extended to systems that can be made passive by pole shiftin