Efstathios N. Antoniou

• BSc, PhD
• Professor (Associate) at International Hellenic University

The ENGINO Toy System introduced two challenging problems. The first was to get bounds on the number of possible models/toys which can be constructed using a given package of building blocks. And the second is to generate automatically the assembly instructions for a given toy. In this report we summarize our insights and provide preliminary result...

During the 125th European Study Group with Industry held in Limassol, Cyprus, 5-9 December 2016, one of the participating companies, Engino.net Ltd, posed a very interesting challenge to the members of the study group. Engino.net Ltd is a Cypriot company, founded in 2004, that produces a series of toy sets -- the Engino$^{\circledR}$ toy sets -- co...

The notion of observability for higher order discrete time systems of algebraic and difference equations is studied. Such systems are also known as Polynomial Matrix Descriptions (PMDs). Attention is first given to a special form of descriptor systems with a state lead in the output. This system is transformed into its causal and noncausal subsyste...

In this paper, a mathematical methodology is presented for the determination of the solution of motion for linear constrained mechanical systems applicable also to systems with singular coefficients. For mathematical completeness and also to incorporate some other interesting cases, the methodology is formulated for a general class of higher order...

An approach is developed based on polynomial matrix theory for formulating the equations of motion and for determining the response of multi-degree-of-freedom (MDOF) linear dynamical systems with singular matrices and subject to linear constraints. This system modeling may appear for reasons such as utilizing redundant DOFs, and can be advantageous...

In the present note, a new characterization of strong linearizations, corresponding to a given regular polynomial matrix, is presented. A linearization of a regular polynomial matrix is a matrix pencil which captures the finite spectral structure of the original matrix, while a strong linearization is one incorporating its structure at infinity alo...

The present article is a survey on linear multivariable systems equivalences. We attempt a review of the most significant forms of system equivalence having as a starting point matrix transformations preserving certain aspects of their spectral structure. From a system theoretic point of view, the need for a variety of forms of polynomial matrix eq...

Descriptor systems provide the natural framework for the study of a wide variety of physical, electrical, mechanical, economical and social systems. In this paper, the response of a Linear Time Invariant (LTI), descriptor system in discrete-time over a finite time interval is examined, whose coefficient matrix on the right hand side of the descript...

Descriptor systems provide the natural framework for the study of a wide variety of physical, electrical, mechanical, economical and social systems. In this paper, the response of a Linear Time Invariant (LTI), descriptor system in discrete-time over a finite time interval is examined, whose coefficient matrix on the right hand side of the descript...

We provide a new approach towards the analysis of the response of higher order systems whose coefficients are subject to norm bounded perturbations. Based on the magnitudes of the perturbations, we obtain bounds of the response of the system. The first order case, that is state space or more generally descriptor systems, has been extensively studie...

We provide a new approach towards the analysis of the response of higher order systems whose coefficients are subject to norm bounded perturbations. Based on the magnitudes of the perturbations, we obtain bounds of the response of the system. The first order case, that is state space or more generally descriptor systems, has been extensively studie...

We provide a new approach towards the analysis of the response of higher order systems whose coefficients are subject to norm bounded perturbations. Based on the magnitudes of the perturbations, we obtain bounds of the response of the system. The first order case - that is, state space or, more generally, descriptor systems - has been extensively s...

In this note we propose a new approach for the construction of a parametrization of the linearizations corresponding to a given polynomial matrix. A linearization of a polynomial matrix is a first order polynomial matrix which is in a certain sense equivalent to the original one. The main advantage of linearization techniques, is that in most cases...

In this note we propose a new approach for the construction of a parametrization of the linearizations corresponding to a given polynomial matrix. A linearization of a polynomial matrix is a first order polynomial matrix which is in a certain sense equivalent to the original one. The main advantage of linearization techniques, is that in most cases...

The present paper is a survey on linear multivariable systems equivalences. We attempt a review of the most significant types of system equivalence having as a starting point matrix transformations preserving certain types of their spectral structure. From a system theoretic point of view, the need for a variety of forms of polynomial matrix equiva...

The algorithm presented in [21] provides a method for the computation of the general solution of a polynomial matrix Diophantine equation. In this work we extend this algorithm for the n-D PMDE.We present a method to efficiently address the division of multivariate polynomials. The theory is implemented via illustrative examples.

We examine the problem of equivalence of discrete time auto-regressive representations (DTARRs) over a finite time interval. Two DTARRs are defined as fundamentally equivalent (FE) over a finite time interval [0,N] if their solution spaces or behaviours are isomorphic. We generalize the concept of strict equivalence (SE) of matrix pencils to the ca...

We examine the problem of equivalence of discrete time auto-regressive representations (DTARRs) over a finite time interval. Two DTARRs are defined as fundamentally equivalent (FE) over a finite time interval [0, N] if their solution spaces or behaviours are isomorphic. We generalize the concept of strict equivalence (SE) of matrix pencils to the c...

In this paper we investigate the behavior of the discrete time AR (Auto Regressive) representations over a finite time interval, in terms of the finite and infinite spectral structure of the polynomial matrix involved in the AR-equation. A boundary mapping equation and a closed formula for the determination of the solution, in terms of the boundary...

In this note we examine the solution and the impulsive behaviour of autonomous linear multivariable systems whose pseudo-state beta(t) obeys a linear matrix differential equation A(rho)beta(t)= 0 where A(rho) is a polynomial matrix in the differential operator rho := d/dt. We thus generalize to the general polynomial matrix case some results obtain...

In this paper we propose a procedure to reduce a 2 - D square polynomial matrix of arbitrary degrees to matrix pencils of the form sX + ZY + A, using zero coprime equivalence. As a further step, we provide the necessary and sufficient condition by which pencils of specific forms, appearing as parametric families, are zero coprime equivalent to a 2...

In Antoniou and Vologiannidis (Electron J Linear Algebra 11:78–87, 2004; 15:107–114, 2006), a new family of companion forms associated with a regular polynomial matrix T (s) has been presented, using products of permutations of n elementary matrices, generalizing similar results presented in Fiedler (Linear Algebra Its Appl 371:325–331, 2003) where...

On the Realization Theory of Polynomial Matrices and the Algebraic Structure of Pure Generalized State Space Systems We review the realization theory of polynomial (transfer function) matrices via "pure" generalized state space system models. The concept of an irreducible-at-infinity generalized state space realization of a polynomial matrix is def...

A collection of algorithms implemented in Mathematica 7.0, freely available over the internet, and capable to manipulate rational functions and solve related control problems using polynomial analysis and design methods is presented. The package provides all the necessary functionality and tools in order to use the theory of W-\it \Omega-stable fun...

It is well known that descriptor systems or generalized state-space systems are the natural framework for the study of physical, electrical mechanical, interconnected, economical and social systems. Although a number of software packages has been developed for state-space systems, which is can be seen as special case of descriptor systems, there ar...

We review the realization theory of polynomial (transfer function) matrices via "pure" generalized state space models. The concept of an irreducible at innity generalized state space realization of a polynomial matrix is dened and the mechanism of the "cancellations" of "decoupling zeros at innity" is closely examined. The difference between the co...

The paper presents a new notion of equivalence of non-regular AR-representations, based on the coincidence of the impulsive-smooth behaviours of the underlying systems. The proposed equivalence is characterized by a special case of the usual unimodular equivalence and a restriction of the matrix transformation of full equivalence (Int. J. Control 1...

The paper presents a new notion of equivalence of non-regular AR- representations, based on the coincidence of the impulsive-smooth behaviors of the underlying systems. The proposed equivalence is characterized by a special case of the usual unimodular equivalence and a restriction of the matrix transformation of full equivalence [21].

In [1] a new family of companion forms associated to a regular polynomial matrix has been presented generalizing similar results presented by M. Fiedler in [2] where the scalar case was considered. This family of companion forms preserves both the …nite and in…nite elementary divisors structure of the original polynomial matrix, thus all its member...

We propose a new algorithm for the computation of a minimal polynomial basis of the left kernel of a given polynomial matrix F(s). The proposed method exploits the structure of the left null space of generalized Wolovich or Sylvester resultants to compute row polynomial vectors that form a minimal polynomial basis of left kernel of the given polyno...

In E.N. Antoniou and S. Vologiannidis ( 2004), a new family of companion forms associated to a regular polynomial matrix has been presented generalizing similar results presented by M. Fiedler in M. Fiedler (2003) where the scalar case was considered. This family of companion forms preserves both the finite and infinite elementary divisors structur...

Given a right coprime MFD of a strictly proper plant P (s) = NR (s) DR (s) -1 with DR (s) column proper a simple numerical algorithm is derived for the computation of of all polynomial solutions [XL (s) , YL (s)] of the polynomial matrix Diophantine equation XL (s) DR (s) + YL (s) NR (s) = DC (s) C (s) := XL (s) -1 YL (s) that when employed in a un...

ó This report describes our joint work on implemen- tation of effective numerical routines for two-variable polyno- mial matrices in the MATHEMATICA software. New functions are connected to the already created program package, being developed at the Czech Technical University in Prague, which calculates only with polynomial matrices in one variable...

The problem of determination of a minimal polyno-mial basis of a rational vector space is the starting point of many control analysis, synthesis and design techniques. In this paper, we propose a new algorithm for the computation of a minimal polynomial basis of the left kernel of a given polynomial matrix F (s). The proposed method exploits the st...

In this paper we present a new family of companion forms associated to a regular polynomial matrix. Similar results have been presented in a recent paper by M. Fiedler [1] where the scalar case is considered. It is shown that the new family of companion forms preserves both the …nite and in…nite elementary divisors structure of the original polynom...

In this note we examine the solution and the impulsive behavior of autonomous linear multivariable systems whose pseudo-state # (t) obeys a linear matrix di#erential equation A (#) # (t) = 0 where A (#) is a polynomial matrix in the di#erential operator # := . We thus generalize to the general polynomial matrix case some results obtained in [2][3]...

We examine the problem of equivalence of discrete time auto-regressive (AR) representations. Two AR representations are defined as fundamentally equivalent if their solution spaces or behaviors are isomorphic. Starting from the fact that the behavior of an AR representation, when considered over a finite time interval, depends on the algebraic stru...

We describe a recently developed integrated software package called Descriptor System Toolbox (DSP), implemented under Mathematica. This new package is fully compatible with two other packages of Mathematica: Control System Professional an add on toolbox of Mathematica that is already in the 1.1 Version and Polynomial Control Systems recently devel...

The main objective of this paper is to determine a closed formula for the forward, backward, and symmetric solution of a general discrete-time Autoregressive Moving Average representation. The importance of this formula is that it is easily implemented in a computer algorithm and gives rise to the solution of analysis, synthesis, and design problem...

The subject of the present PhD thesis is the study of singular linear discrete time systems. The regular first-order case has been studied by several authors in the past, mainly in an algebraic and geometric analysis level. The main objective of the present study is to extend these results towards three directions. In particular, the analysis of no...

The subject of the present PhD thesis is the study of singular linear discrete time systems. The regular first-order case has been studied by several authors in the past, mainly in an algebraic and geometric analysis level. The main objective of the present study is to extend these results towards three directions. In particular, the analysis of no...

In this note we study the e#ect of constant pseudostate feedback on the internal properness of a linear multivariable system, described by an ARMA model. It is shown that the existence of a constant pseudostate feedback control law which makes the closed loop system internally proper is equivalent to the absence of decoupling zeros at infinity of t...

In this note we examine the solution and the impulsive behaviour of autonomous linear multivariable systems whose pseudo-state β(t) obeys a linear matrix differential equation A(ρ)β(t) = 0 where A(ρ) is a polynomial matrix in the differential operator ρ := d/dt. We thus generalize to the general polynomial matrix case some results obtained by Vergh...

A classification of the solutions of linear, time invariant non-regular, discrete descriptor systems is given in terms of the structural invariant of the associated matrix pencil σE-A. The lack of conditionability (in the general case) implies a partitioning of the behavior and thus a classification of the solution according to their boundary value...

In this paper we investigate the behavior of the discrete time AR (Auto Regressive) representations over a finite time interval, in terms of the finite and infinite spectral structure of the polynomial matrix involved in the AR-equation. A boundary mapping equation and a closed formula for the determination of the solution, in terms of the boundary...

The algorithms required for the solution of several problems in the study of linear multivariable systems, can be proved to be a very tedious task and usually only a few trivial examples can be entirely worked out manually in a reasonable time. A package containing some basic algorithms for the study of linear systems, implemented via Maple V, is p...