Dimitris Vafiadis

Canonical forms for descriptor systems under restricted system equivalence

Abstract The problem of canonical forms of implicit descriptor systems under restricted system equivalence is considered. It is shown that the canonical form is directly related to the echelon form of the autoregressive matrix inducing the external behavior of the system. The proposed canonical form is a generalization of the Popov form, and is also valid for singular systems, under transfer equivalence.

Decoupling and pole assignment of singular systems: a frequency domain approach

Abstract A new approach to the row by row decoupling of singular systems via state feedback and regular input transformation is presented. The proposed method is based on the matrix fraction description of the system and is an extension of the frequency domain method for strictly proper systems. The solvability condition of the problem is readily obtained from the ‘numerator’ matrix of a coprime and column reduced matrix fraction description of the given system. Pole placement and decoupling is also considered, and the characterization of the fixed poles is given.

Generalized state-space realizations from matrix fraction descriptions

The problem of the realization of a matrix fraction description (MFD) of a nonproper transfer function is considered. An algorithm for the realization is developed, and it is shown that it is a natural generalization of Wolovichs method (1973) for the case of proper systems. The resulting generalized state-space system is shown to be reachable, and the conditions for its minimality, in terms of the coprimeness and column reducedness of the MFD, are derived. The relation between the controllability indexes of the realization and the Forney order (1975) of the MFD is established. >

Disturbance and input-output decoupling of singular systems

The disturbance decoupling and the simultaneous disturbance and input-output decoupling problems for singular systems are considered in the context of the matrix fraction description (MFD) of the system. Solvability conditions are obtained in terms of the composite matrix of a column reduced MFD of the system, a characterisation of the fixed poles of both problems is given and it is shown that the remaining poles can be arbitrarily assigned.

First-order realizations of autoregressive equations

The problem of first-order realizations of autoregressive equations under external equivalence is considered and new realization methods are presented. These realizations are obtained from the coefficients of the polynomial entries of the autoregressive matrix of thegiven system. The treatment of the problem involves only polynomial matrix arguments, in a way analogous to the realization methods from matrix fraction descriptions of transfer functions into state space models.

Model matching under external and input-output equivalence

The model-matching problem for systems described by external models is considered in frameworks of both external and input-output equivalence. Necessary conditions for the solvability of the problem are produced, and it is shown that in certain cases these conditions are also sufficient. In the case where necessary and sufficient conditions exist, the solutions of the problem are obtained in a constructive way and a parametrization of solutions is given.

Unimodular equivalence and similarity for linear systems

ABSTRACT The problem of finding the mapping between unimoduar transformations relating two minimal matrix fraction descriptions (MFDs) of a transfer function, and the similarity transformations relating the respective minimal state-space representations is considered. It is shown that the problem is equivalent to finding the relation of MFDs of the input-state transfer functions of the two systems. This relation turns out to be an equivalence relation involving the unimodular and the similarity matrices relating the MFDs and the state-space systems, respectively. A canonical form for MFDs under this equivalence relation is obtained and it is shown that it leads to a canonical state-space representation, via a realisation procedure.

Disturbance and Input - Output Decoupling of Singular Systems

Abstract The disturbance decoupling and the simulteneous disturbance and input – output decoupling problems for singular systems are considered in the context of the matrix fraction description (MFD) of the system. Solvability conditions are obtained in terms of the composite matrix of a column reduced MFD of the system, a characterisation of the fixed poles of both problems is given and it is shown that the remaining poles can be arbitrarily assigned.