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Elimination of finite eigenvalues of the 2D Roesser model by state feedbacks

Tadeusz Kaczorek (2001)

International Journal of Applied Mathematics and Computer Science

A new problem of decreasing the degree of the closed-loop characteristic polynomial of the 2D Roesser model by a suitable choice of state feedbacks is formulated. Sufficient conditions are established under which it is possible to choose state feedbacks such that the non-zero closed-loop characteristic polynomial has degree zero. A procedure for computation of the feedback gain matrices is presented and illustrated by a numerical example.

Enlarged Asymptotic Compensation in Discrete Distributed Systems

L. Afifi, M. Hakam, M. Bahadi, A. El Jai (2010)

Mathematical Modelling of Natural Phenomena

This work concerns an enlarged analysis of the problem of asymptotic compensation for a class of discrete linear distributed systems. We study the possibility of asymptotic compensation of a disturbance by bringing asymptotically the observation in a given tolerance zone 𝒞. Under convenient hypothesis, we show the existence and the unicity of the optimal control ensuring this compensation and we give its characterization

Equivalent descriptions of a discrete-time fractional-order linear system and its stability domains

Piotr Ostalczyk (2012)

International Journal of Applied Mathematics and Computer Science

Two description forms of a linear fractional-order discrete system are considered. The first one is by a fractional-order difference equation, whereas the second by a fractional-order state-space equation. In relation to the two above-mentioned description forms, stability domains are evaluated. Several simulations of stable, marginally stable and unstable unit step responses of fractional-order systems due to different values of system parameters are presented.

Event monitoring of parallel computations

Alexander M. Gruzlikov, Nikolai V. Kolesov, Marina V. Tolmacheva (2015)

International Journal of Applied Mathematics and Computer Science

The paper considers the monitoring of parallel computations for detection of abnormal events. It is assumed that computations are organized according to an event model, and monitoring is based on specific test sequences.

Existence of different kind of solutions for discrete time equations

Denis Pennequin (2014)

Nonautonomous Dynamical Systems

The aim of this paper is to extend the classical linear condition concerning diagonal dominant bloc matrix to fully nonlinear equations. Even if assumptions are strong, we obtain an explicit condition which exactly extend the one known in linear case, and the setting allows also to consider bicontinuous operator instead of the schift and as particular case, we receive periodic or almost periodic solutions for discrete time equations.

Externally and internally positive singular discrete-time linear systems

Tadeusz Kaczorek (2002)

International Journal of Applied Mathematics and Computer Science

Notions of externally and internally positive singular discrete-time linear systems are introduced. It is shown that a singular discrete-time linear system is externally positive if and only if its impulse response matrix is non-negative. Sufficient conditions are established under which a single-output singular discrete-time system with matrices in canonical forms is internally positive. It is shown that if a singular system is weakly positive (all matrices E, A, B, C are non-negative), then it...

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