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Some remarks on matrix pencil completion problems

Jean-Jacques Loiseau, Petr Zagalak, Sabine Mondié (2004)

Kybernetika

The matrix pencil completion problem introduced in [J. J. Loiseau, S. Mondié, I. Zaballa, and P. Zagalak: Assigning the Kronecker invariants to a matrix pencil by row or column completions. Linear Algebra Appl. 278 (1998)] is reconsidered and the latest results achieved in that field are discussed.

SPR0 substitutions and families of algebraic Riccati equations

G. Fernández-Anaya, J. C. Martínez García, Vladimír Kučera, D. Aguilar George (2006)

Kybernetika

We study in this paper Algebraic Riccati Equations associated with single-input single-output linear time-invariant systems bounded in H -norm. Our study is focused in the characterization of families of Algebraic Riccati Equations in terms of strictly positive real (of zero relative degree) substitutions applied to the associated H -norm bounded system, each substitution characterizing then a particular member of the family. We also consider here Algebraic Riccati Equations associated with systems...

State elimination for nonlinear neutral state-space systems

Miroslav Halás, Pavol Bisták (2014)

Kybernetika

The problem of finding an input-output representation of a nonlinear state space system, usually referred to as the state elimination, plays an important role in certain control problems. Though, it has been shown that such a representation, at least locally, always exists for both the systems with and without delays, it might be a neutral input-output differential equation in the former case, even when one starts with a retarded system. In this paper the state elimination is therefore extended...

State-space realization of nonlinear control systems: unification and extension via pseudo-linear algebra

Juri Belikov, Ülle Kotta, Maris Tõnso (2012)

Kybernetika

In this paper the tools of pseudo-linear algebra are applied to the realization problem, allowing to unify the study of the continuous- and discrete-time nonlinear control systems under a single algebraic framework. The realization of nonlinear input-output equation, defined in terms of the pseudo-linear operator, in the classical state-space form is addressed by the polynomial approach in which the system is described by two polynomials from the non-commutative ring of skew polynomials. This allows...

The algebraic structure of delay-differential systems: a behavioral perspective

Heide Glüsing-Lüerssen, Paolo Vettori, Sandro Zampieri (2001)

Kybernetika

This paper presents a survey on the recent contributions to linear time- invariant delay-differential systems in the behavioral approach. In this survey both systems with commensurate and with noncommensurate delays will be considered. The emphasis lies on the investigation of the relationship between various systems descriptions. While this can be understood in a completely algebraic setting for systems with commensurate delays, this is not the case for systems with noncommensurate delays. In the...

The tracking and regulation problem for a class of generalized systems

Antonio Tornambè (1998)

Kybernetika

The tracking and regulation problem is considered for a class of generalized systems, in case of exponential reference signals and of disturbance functions. First, the notions of steady-state response and of blocking zero, which are classical for linear time-invariant systems, are given for generalized systems. Then, the tracking and regulation problem is stated and solved for the class of generalized systems under consideration, giving a general design procedure. As a corollary of the effectiveness...

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