Three theorems on hierarchical decomposition of similarity linear systems

In this paper the problem of system decomposition of complex linear dynamical systems biy exploiting the similarity property is studied. System decompositions are sought in terms of similarity hierarchical structures. The method for constructing the transformation is derived. The conditions for such decomposition of complex linear systems are given.

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MODELING LINEAR DYNAMICAL SYSTEMS BY CONTINUOUS-VALUED CELLULAR AUTOMATA

International Journal of Modern Physics C ◽

10.1142/s0129183107010589 ◽

2007 ◽

Vol 18 (05) ◽

pp. 833-848 ◽

Cited By ~ 2

Author(s):

JUAN CARLOS SECK TUOH MORA ◽

MANUEL GONZALEZ HERNANDEZ ◽

NORBERTO HERNANDEZ ROMERO ◽

AARON RODRIGUEZ TREJO ◽

SERGIO V. CHAPA VERGARA

Keyword(s):

Dynamical System ◽

Dynamical Systems ◽

Cellular Automata ◽

Linear Systems ◽

Configuration Space ◽

Integration Method ◽

Numerical Calculations ◽

Linear Dynamical Systems ◽

Original Part

This paper exposes a procedure for modeling and solving linear systems using continuous-valued cellular automata. The original part of this work consists on showing how the cells in the automaton may contain both real values and operators for carrying out numerical calculations and solve a desired problem. In this sense the automaton acts as a program, where data and operators are mixed in the evolution space for obtaining the correct calculations. As an example, Euler's integration method is implemented in the configuration space in order to achieve an approximated solution for a dynamical system. Three examples showing linear behaviors are presented.

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BIMODAL PIECEWISE LINEAR DYNAMICAL SYSTEMS: REDUCED FORMS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127410027362 ◽

2010 ◽

Vol 20 (09) ◽

pp. 2795-2808 ◽

Cited By ~ 7

Author(s):

JOSEP FERRER ◽

M. DOLORS MAGRET ◽

MARTA PEÑA

Keyword(s):

Dynamical Systems ◽

Linear Systems ◽

Piecewise Linear ◽

Equivalence Classes ◽

State Variables ◽

Linear Dynamical Systems ◽

Piecewise Linear Systems ◽

Wide Range ◽

General Systems ◽

Reduced Forms

Piecewise linear systems constitute a class of nonlinear systems which have recently attracted the interest of researchers because of their interesting properties and the wide range of applications from which they arise. Different authors have used reduced forms when studying these systems, mostly in the case where they are observable. In this work, we focus on bimodal continuous dynamical systems (those consisting of two linear systems on each side of a given hyperplane, having continuous dynamics along that hyperplane) depending on two or three state variables, which are the most common piecewise linear systems found in practice. Reduced forms are obtained for general systems, not necessarily observable. As an application, we calculate the dimension of the equivalence classes.

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Linear Dynamical Systems of Higher Genus

Georgian Mathematical Journal ◽

10.1515/gmj.1994.505 ◽

1994 ◽

Vol 1 (5) ◽

pp. 505-521

Author(s):

V. Lomadze

Keyword(s):

Dynamical Systems ◽

Linear Systems ◽

Rational Function ◽

Function Field ◽

Algebraic Function ◽

Linear Dynamical Systems ◽

Algebraic Function Field ◽

Rational Function Field ◽

Higher Genus

Abstract A class of linear systems which after ordinary linear systems are in a certain sense the simplest ones, is associated with every algebraic function field. From the standpoint developed in the paper ordinary linear systems are associated with the rational function field.

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On the Efficacy of Nonlinear Control in Uncertain Linear Systems

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.3139661 ◽

1981 ◽

Vol 103 (2) ◽

pp. 95-102 ◽

Cited By ~ 296

Author(s):

G. Leitmann

Keyword(s):

Dynamical Systems ◽

Feedback Control ◽

Nonlinear Control ◽

Linear Systems ◽

Linear Feedback ◽

System Response ◽

Linear Feedback Control ◽

Linear Dynamical Systems ◽

Uncertain Linear Systems ◽

Measured State

We consider a class of linear dynamical systems containing uncertain elements and subject to uncertain inputs, and for which either uncertain state or output is available. We construct a feedback control, utilizing measured state or estimated state, which guarantees that every system response is ultimately bounded within a certain neighborhood of the zero state. Performance resulting from use of this control is compared with that due to the use of purely linear feedback control.

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Designing the mesoscopic approach of an autonomous linear dynamical system by a quantum formulation

Libro de Actas - Systems & Design: Beyond Processes and Thinking (IFDP - SD2016) ◽

10.4995/ifdp.2016.2795 ◽

2016 ◽

Author(s):

Juan Carlos Micó Ruiz

Keyword(s):

Dynamical System ◽

Dynamical Systems ◽

Linear Systems ◽

Second Order ◽

Linear Dynamical System ◽

Linear Dynamical Systems ◽

General Systems ◽

Non Linear ◽

Quantum Formulation

The work presents a mesoscopic approach to general systems modelled by dynamical systems. The quantum formulation is possible to be obtained by their quantum formulation from a second order Hamiltonian. However, only autonomous linear systems are proved to obtain a Hamiltonian like this. Some application cases are presented, and a discussion about how to generalize the formalism to non-linear dynamical systems is sketched.DOI: http://dx.doi.org/10.4995/IFDP.2016.2795

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Controllability Subspaces of Multi-Aagent Linear Dynamical Systems

WSEAS TRANSACTIONS ON CIRCUITS AND SYSTEMS ◽

10.37394/23201.2021.20.20 ◽

2021 ◽

Vol 20 ◽

pp. 166-172

Author(s):

M. I. Garcia-Planas

Keyword(s):

Dynamical Systems ◽

Linear Systems ◽

Multiagent Systems ◽

Invariant Subspaces ◽

Communication Channels ◽

Multi Agent Systems ◽

Linear Dynamical Systems ◽

Agent Systems ◽

Multi Agent ◽

Controllability Subspaces

This work addresses the controllability subspaces of a class of multi-agent linear systems that are interconnected via communication channels. Multiagent systems have attracted much attention because they have great applicability in multiple areas. Recently has taken an interest to analyze the control properties as consensus controllability of multi-agent dynamical systems motivated by the fact that the architecture of communication network in engineering multi-agent systems is usually adjustable. In this paper, the concept of invariant subspaces and controllability subspaces is reviewed and generalized to multi-agent systems. Finally, the consensus controllability subspaces are analyzed in the case of multiagent linear systems having all agents the same dynamics described as xi = Aixi + Biui, i = 0, 1, . . . , k.

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