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The paper aims at formulating an integrated approach for the selection of decentralized control structures using a number of structural criteria aiming at facilitating the design of decentralised control schemes. This requires the selection of decentralisation structure that will allow the generic solvability of a variety of decentralised control problems, such as pole assignment by decentralised output feedback. The approach is based on the use of necessary and sufficient conditions for generic solvability and exact solvability of decentralised control problems. The generic solvability conditions lead to characterisations of inputs and outputs channel partitions. The exact solvability conditions use criteria on avoiding the presence of fixed modes, as well as necessary conditions for pole assignment, expressed in terms of properties of Plϋcker invariants and Markov type matrices. The structural approach provides a classification of desirable input and output partitions based on structural criteria and it is embedded in an overall framework that may involve aspects related to large scale design.

Linear Control Theory problems such as those of pole assignment by state, output feedback (centralised or decentralised), and zero assignment by input, or output squaring down may be reduced to a standard common problem known as the Determinantal assignment Problem (DAP) Giannakopoulos (1985). The aim of this paper is to develop and compare optimization algorithms for the computation of solutions of DAP. The developed numerical approaches may be used as a basis of a design technique centered around the frequency assignment problems.

The McMillan degree of a transfer fimction model is one of the most important structural characteristics and plays an important role in deciding about the quality of a system model, as far as aollowing solvability of certain control ptoblems. In this paper the problem of identifying the generic McMillan degree of a rational matrix is considered The transfer function matrices of interest are those referred to as Structured Transfer Function (STF) matrices and have certain elements fixed to zero, some elements being constant and other elements expressing some identified dominant dynamics of the system. For the family of STF matrices the problem of determining the generic McMillan degree is considered using genericity arguments and an optimisation procedure based on path properties of nonnegative integer matrices. A novel approach is introduced using the notion of irreducibility of nonnegative matrices which leads to an efficient new algorithm for computation of the generic value of the McMillan degree. Links to standard problems of graph theory are made. The problem examined here belongs to the general area of Structural Identification where the evaluation of structural characteristics of STF models is under investigation with robust computational methods. Such problems are of specific interest to large scale systems.

A special case of the simultaneous stabilization problem, namely the stabilization in Finite Settling Time (FST) sense of a family of discrete-time plants by a single compensator is examined in this paper. Necessary and/or sufficient solvability conditions for the general MIMO case are given and testable conditions for the case of vector plants are derived. Finally, the problem of simultaneous FST stabilization and tracking is considered for the case of vector plants.