Necessary and sufficient conditions are found for there to exist a robust controller for a linear, time-invariant, multivariable system (plant) so that asymptotic tracking/regulation occurs independent of input disturbances and arbitrary perturbations in the plant parameters of the system. In this problem, the class of plant parameter perturbations allowed is quite large; in particular, any perturbations in the plant data are allowed as long as the resultant closed-loop system remains stable. A complete characterization of all such robust controllers is made. It is shown that any robust controller must consist of two devices 1) a servocompensator and 2) a stabilizing compensator. The servocompensator is a feedback compensator with error input consisting of a number of unstable subsystems (equal to the number of outputs to be regulated) with identical dynamics which depend on the disturbances and reference inputs to the system. The sorvocompensator is a compensator in its own right, quite distinct from an observer and corresponds to a generalization of the integral controller of classical control theory. The sole purpose of the stabilizing compensator is to stabilize the resultant system obtained by applying the servocompensator to the plant. It is shown that there exists a robust controller for "almost all" systems provided that the number of independent plant inputs is not less than the number of independent plant outputs to be regulated, and that the outputs to be regulated are contained in the measurable outputs of the system; if either of these two conditions is not satisfied, there exists no robust controller for the system.

The robust control of a servomechanism problem for linear time-invariant multivariable systems

This paper surveys the control theoretic literature on decentralized and hierarchical control, and methods of analysis of large scale systems.

Survey of decentralized control methods for large scale systems

Introduction to systems general properties of linear systems the geometric approach - analysis, synthesis, robustness optimality.

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Controlled and conditioned invariants in linear system theory

Survey Generic properties and control of linear structured systems: a survey

This survey is concerned with the definition and main properties of sets of specific values of complex frequency, called poles and zeros, which may be associated with a matrix-valued function of a complex frequency variable. The main emphasis is on the physical interpretation of invariant zeros in terms of the general zero-output behaviour of a linear dynamical system. A discussion is given of the relationship between this definition of a zero and the various other forms adopted in the current literature. The relationship is considered between poles and zeros defined by algebraic means and the standard complex variable theory of algebraic functions. It is shown that the poles and zeros of a square matrix-valued function of a complex variable G(s) are the same as the poles and zeros of an associated algebraic function g(s).

S. H. Wang

Papers

Properties and calculation of transmission zeros of linear multivariable systems

Correspondence item: Remark on multiple transmission zeros of a system