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Canonical forms of singular 1D and 2D linear systems

Tadeusz Kaczorek (2003)

International Journal of Applied Mathematics and Computer Science

The paper consists of two parts. In the first part, new canonical forms are defined for singular 1D linear systems and a procedure to determine nonsingular matrices transforming matrices of singular systems to their canonical forms is derived. In the second part new canonical forms of matrices of the singular 2D Roesser model are defined and a procedure for determining realisations in canonical forms for a given 2D transfer function is presented. Necessary and sufficient conditions for the existence...

Canonical input-output representation of linear multivariable stochastic systems and joint optimal parameter and state estimation.

G. Salut, J. Aguilar-Martín, S. Lefevre (1979)

Stochastica

In this paper a complete presentation is given of a new canonical representation of multi-input, multi-output linear stochastic systems. Its equivalence with operator form directly linked with ARMA processes as well as with classical state space representation is given, and a transfer matrix interpretation is developed in an example. The importance of the new representation is mainly in the fact that in the joint state and parameters estimation problem, all unknown parameters appear linearly when...

Characterization of generic properties of linear structured systems for efficient computations

Christian Commault, Jean-Michel Dion, Jacob W. van der Woude (2002)

Kybernetika

In this paper we investigate some of the computational aspects of generic properties of linear structured systems. In such systems only the zero/nonzero pattern of the system matrices is assumed to be known. For structured systems a number of characterizations of so-called generic properties have been obtained in the literature. The characterizations often have been presented by means of the graph associated to a linear structured system and are then expressed in terms of the maximal or minimal...

Closed-loop structure of decouplable linear multivariable systems

Javier Ruiz, Jorge Luis Orozco, Ofelia Begovich (2005)

Kybernetika

Considering a controllable, square, linear multivariable system, which is decouplable by static state feedback, we completely characterize in this paper the structure of the decoupled closed-loop system. The family of all attainable transfer function matrices for the decoupled closed-loop system is characterized, which also completely establishes all possible combinations of attainable finite pole and zero structures. The set of assignable poles as well as the set of fixed decoupling poles are determined,...

Computation of realizations composed of dynamic and static parts of improper transfer matrices

Tadeusz Kaczorek (2007)

International Journal of Applied Mathematics and Computer Science

The problem of computing minimal realizations of a singular system decomposed into a standard dynamical system and a static system of a given improper transfer matrix is formulated and solved. A new notion of the minimal dynamical-static realization is introduced. It is shown that there always exists a minimal dynamical-static realization of a given improper transfer matrix. A procedure for the computation of a minimal dynamical-static realization for a given improper transfer matrix is proposed...

Condiciones algebraicas de existencia y estabilidad para el diseño de controladores para sistemas lineales multivariables interconectados.

Manuel de la Sen (1986)

Stochastica

This paper presents an algebraic design theory for interconnected systems. Usual multivariable linear systems are described in a unified way. Both square and nonsquare plants and controllers are included in the study and an easy characterization of the achievable I/O (input-to-output) and D/O (disturbance-to-output) maps is presented through the use of appropriate controllers. Sufficient conditions of stability are given.

Cone-type constrained relative controllability of semilinear fractional systems with delays

Beata Sikora, Jerzy Klamka (2017)

Kybernetika

The paper presents fractional-order semilinear, continuous, finite-dimensional dynamical systems with multiple delays both in controls and nonlinear function f . The constrained relative controllability of the presented semilinear system and corresponding linear one are discussed. New criteria of constrained relative controllability for the fractional semilinear systems with delays under assumptions put on the control values are established and proved. The conical type constraints are considered....

Construction of algebraic and difference equations with a prescribed solution space

Lazaros Moysis, Nicholas P. Karampetakis (2017)

International Journal of Applied Mathematics and Computer Science

This paper studies the solution space of systems of algebraic and difference equations, given as auto-regressive (AR) representations A(σ)β(k) = 0, where σ denotes the shift forward operator and A(σ) is a regular polynomial matrix. The solution space of such systems consists of forward and backward propagating solutions, over a finite time horizon. This solution space can be constructed from knowledge of the finite and infinite elementary divisor structure of A(σ). This work deals with the inverse...

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