scholarly journals On the regulator problem for linear systems over rings and algebras

2021 ◽  
Vol 19 (1) ◽  
pp. 101-110
Author(s):  
José Ángel Hermida-Alonso ◽  
Miguel V. Carriegos ◽  
Andrés Sáez-Schwedt ◽  
Tomás Sánchez-Giralda
Keyword(s):  
Dynamical System ◽  
Linear Systems ◽  
Commutative Rings ◽  
Canonical System ◽  
Linear Dynamical System ◽  
Regulator Problem ◽  
Observable System ◽  
Ring Of Fractions ◽  
Systems Over Rings ◽  
Rings And Algebras

Abstract The regulator problem is solvable for a linear dynamical system Σ \Sigma if and only if Σ \Sigma is both pole assignable and state estimable. In this case, Σ \Sigma is a canonical system (i.e., reachable and observable). When the ring R R is a field or a Noetherian total ring of fractions the converse is true. Commutative rings which have the property that the regulator problem is solvable for every canonical system (RP-rings) are characterized as the class of rings where every observable system is state estimable (SE-rings), and this class is shown to be equal to the class of rings where every reachable system is pole-assignable (PA-rings) and the dual of a canonical system is also canonical (DP-rings).

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

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

A novel unified approach to invariance conditions for a linear dynamical system

2017 ◽  
Vol 298 ◽  
pp. 351-367 ◽  
Author(s):  
Zoltán Horváth ◽  
Yunfei Song ◽  
Tamás Terlaky
Keyword(s):  
Dynamical System ◽  
Linear Dynamical System ◽  
Unified Approach

scholarly journals Communicating vessels: a non-linear dynamical system

2017 ◽  
Vol 39 (3) ◽  
Author(s):  
Roberto De Luca ◽  
Orazio Faella
Keyword(s):  
Dynamical System ◽  
Fluid Flow ◽  
Ideal Fluid ◽  
Oscillatory Motion ◽  
Linear Dynamical System ◽  
Static Properties ◽  
Bernoulli’S Equation ◽  
Non Linear ◽  
Dynamical Properties

The dynamics of an ideal fluid contained in two communicating vessels is studied. Despite the fact that the static properties of this system have been known since antiquity, the knowledge of the dynamical properties of an ideal fluid flowing in two communicating vessels is not similarly widespread. By means of Bernoulli's equation for non-stationary fluid flow, we study the oscillatory motion of the fluid when dissipation can be neglected.

scholarly journals Duality for linear systems over rings

1981 ◽  
Vol 50 (1) ◽  
pp. 85-90
Author(s):  
G. Naud ◽  
C. Nolte
Keyword(s):  
Linear Systems ◽  
Systems Over Rings

MODELING LINEAR DYNAMICAL SYSTEMS BY CONTINUOUS-VALUED CELLULAR AUTOMATA

2007 ◽  
Vol 18 (05) ◽  
pp. 833-848 ◽  
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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