scholarly journals Reachability of linear hybrid systems described by the general model

2010 ◽  
Vol 20 (2) ◽  
pp. 199-207 ◽  
Author(s):  
Tadeusz Kaczorek ◽  
Krzysztof Rogowski
Keyword(s):  
Linear Systems ◽  
Hybrid Systems ◽  
Hybrid System ◽  
General Model ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sufficient Condition ◽  
Numerical Examples ◽  
Necessary And Sufficient

Reachability of linear hybrid systems described by the general modelThe reachability of standard and positive hybrid linear systems described by the general model is addressed. Necessary and sufficient conditions for the reachability of the standard general model are established. Sufficient condition is given for the reachability of positive hybrid system described by the general model. The considerations are illustrated by numerical examples.

Asymptotic stability of positive 2D linear systems with delays

2009 ◽  
Vol 57 (2) ◽  
pp. 133-138 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Asymptotic Stability ◽  
Linear Systems ◽  
General Model ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Roesser Model ◽  
Numerical Examples ◽  
Necessary And Sufficient

Asymptotic stability of positive 2D linear systems with delays New necessary and sufficient conditions for the asymptotic stability of positive 2D linear systems with delays described by the general model, Fornasini-Marchesini models and Roesser model are established. It is shown that checking of the asymptotic stability of positive 2D linear systems with delays can be reduced to the checking of the asymptotic stability of corresponding positive 1D linear systems without delays. The efficiency of the new criterions is demonstrated on numerical examples.

Normal and Quasi-Normal Modes in Damped Linear Dynamic Systems

1966 ◽  
Vol 33 (2) ◽  
pp. 413-416 ◽  
Author(s):  
J. S. Maybee
Keyword(s):  
Linear Systems ◽  
Dynamic Systems ◽  
Normal Modes ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Linear Dynamic Systems ◽  
Linear Dynamic ◽  
Necessary And Sufficient

A generalization of the concept of classical normal modes in damped linear systems is presented. It is then shown that a necessary and sufficient condition that such quasi-normal modes exist is that certain matrices associated with the system commute. Necessary and sufficient conditions of the same type are also obtained for the classical normal modes, but under more restrictive conditions.

scholarly journals Reduced-order fractional descriptor observers for fractional descriptor continuous-time linear system

2014 ◽  
Vol 62 (4) ◽  
pp. 889-895 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Design Procedure ◽  
Necessary And Sufficient Conditions ◽  
Reduced Order ◽  
Numerical Examples ◽  
Necessary And Sufficient ◽  
Time Linear

Abstract Fractional descriptor reduced-order observers for fractional descriptor continuous-time linear systems are proposed. Necessary and sufficient conditions for the existence of the observers are established. The design procedure of the observers is given and is demonstrated on two numerical examples.

scholarly journals A convergence analysis of SOR iterative methods for linear systems with weak H-matrices

2016 ◽  
Vol 14 (1) ◽  
pp. 747-760
Author(s):  
Cheng-yi Zhang ◽  
Zichen Xue ◽  
Shuanghua Luo
Keyword(s):  
Convergence Analysis ◽  
Linear Systems ◽  
Iterative Methods ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Numerical Examples ◽  
Convergence Results ◽  
Diagonally Dominant Matrices ◽  
Diagonally Dominant ◽  
Necessary And Sufficient

AbstractIt is well known that SOR iterative methods are convergent for linear systems, whose coefficient matrices are strictly or irreducibly diagonally dominant matrices and strong H-matrices (whose comparison matrices are nonsingular M-matrices). However, the same can not be true in case of those iterative methods for linear systems with weak H-matrices (whose comparison matrices are singular M-matrices). This paper proposes some necessary and sufficient conditions such that SOR iterative methods are convergent for linear systems with weak H-matrices. Furthermore, some numerical examples are given to demonstrate the convergence results obtained in this paper.

scholarly journals Robust stability of positive continuous-time linear systems with delays

2010 ◽  
Vol 20 (4) ◽  
pp. 665-670 ◽  
Author(s):  
Mikołaj Busłowicz
Keyword(s):  
Linear Systems ◽  
Robust Stability ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Numerical Examples ◽  
Structured Perturbations ◽  
Uncertainty Structure ◽  
Necessary And Sufficient ◽  
Time Linear

Robust stability of positive continuous-time linear systems with delaysThe paper is devoted to the problem of robust stability of positive continuous-time linear systems with delays with structured perturbations of state matrices. Simple necessary and sufficient conditions for robust stability in the general case and in the case of systems with a linear uncertainty structure in two sub-cases: (i) a unity rank uncertainty structure and (ii) nonnegative perturbation matrices are established. The problems are illustrated with numerical examples.

scholarly journals Fractional descriptor observers for fractional descriptor continuous-time linear system

2014 ◽  
Vol 24 (1) ◽  
pp. 27-37 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Design Procedure ◽  
Necessary And Sufficient Conditions ◽  
Numerical Examples ◽  
Necessary And Sufficient ◽  
Time Linear

Abstract Fractional descriptor full-order observers for fractional descriptor continuous-time linear systems are proposed. Necessary and sufficient conditions for the existence of the observers are established. The design procedure of the observers is demonstrated on two numerical examples.

scholarly journals New stability conditions for positive continuous-discrete 2D linear systems

2011 ◽  
Vol 21 (3) ◽  
pp. 521-524 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Asymptotic Stability ◽  
Linear Systems ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Stability Conditions ◽  
Stability Tests ◽  
Numerical Examples ◽  
The Stability ◽  
Necessary And Sufficient

New stability conditions for positive continuous-discrete 2D linear systemsNew necessary and sufficient conditions for asymptotic stability of positive continuous-discrete 2D linear systems are established. Necessary conditions for the stability are also given. The stability tests are demonstrated on numerical examples.

Stability of continuous-discrete linear systems described by the general model

2011 ◽  
Vol 59 (2) ◽  
pp. 189-193 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Asymptotic Stability ◽  
Linear Systems ◽  
General Model ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Discrete Linear Systems ◽  
Necessary And Sufficient ◽  
2D Model

Stability of continuous-discrete linear systems described by the general modelNew necessary and sufficient conditions for asymptotic stability of positive continuous-discrete linear systems described by the general 2D model are established. A procedure for checking the asymptotic stability is proposed. The effectiveness of the procedure is demonstrated on examples.

scholarly journals Stability of continuous-discrete linear systems with delays in state vector

2011 ◽  
Vol 21 (1) ◽  
pp. 25-36
Author(s):  
Tadeusz Kaczorek ◽  
Łukasz Sajewski
Keyword(s):  
Asymptotic Stability ◽  
Linear Systems ◽  
General Model ◽  
State Vector ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Numerical Example ◽  
New Class ◽  
Discrete Linear Systems ◽  
Necessary And Sufficient

Stability of continuous-discrete linear systems with delays in state vector A new class of positive continuous-discrete linear systems with delays in state vector described by the model based on 2D general model is addressed. Necessary and sufficient conditions for the positivity and asymptotic stability of this class of linear systems are established. A procedure for checking the asymptotic stability is proposed. The effectiveness of the procedure is demonstrated on a numerical example.

Positive fractional continuous-time linear systems with singular pencils

2012 ◽  
Vol 60 (1) ◽  
pp. 9-12 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Descriptor Systems ◽  
State Variables ◽  
Algebraic Constraints ◽  
Necessary And Sufficient ◽  
Time Linear

Positive fractional continuous-time linear systems with singular pencils A method for checking the positivity and finding the solution to the positive fractional descriptor continuous-time linear systems with singular pencils is proposed. The method is based on elementary row and column operations of the fractional descriptor systems to equivalent standard systems with some algebraic constraints on state variables and inputs. Necessary and sufficient conditions for the positivity of the fractional descriptor systems are established.

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