Existence of Metzler Matrices with Given Spectra of Positive Stable Linear Systems and Electrical Circuits

2016 ◽  
pp. 141-154
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Electrical Circuits ◽  
Stable Linear

Coprime Factorizations in Stable Linear Systems

1988 ◽  
Author(s):  
Charles A. Desoer ◽  
A. Nazli Gundes ◽  
M. Guntekin Kabuli
Keyword(s):  
Linear Systems ◽  
Coprime Factorizations ◽  
Stable Linear

Quantized control of stochastic stable linear systems

1999 ◽  
Vol 32 (2) ◽  
pp. 4971-4976
Author(s):  
K.-S. Lee ◽  
A.H. Haddad
Keyword(s):  
Linear Systems ◽  
Quantized Control ◽  
Stable Linear

scholarly journals Time-Varying Vector Norm and Lower and Upper Bounds on the Solutions of Uniformly Asymptotically Stable Linear Systems

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 915
Author(s):  
Robert Vrabel
Keyword(s):  
Linear Systems ◽  
Linear Time ◽  
Upper Bounds ◽  
Time Varying ◽  
Asymptotically Stable ◽  
Lower And Upper Bounds ◽  
Linear Time Invariant ◽  
Vector Norm ◽  
Linear Time Invariant Systems ◽  
Stable Linear

Based on the eigenvalue idea and the time-varying weighted vector norm in the state space R n we construct here the lower and upper bounds of the solutions of uniformly asymptotically stable linear systems. We generalize the known results for the linear time-invariant systems to the linear time-varying ones.

The Optimal Switched Law Methods Analysis and Research on Switched Linear Systems

2012 ◽  
Vol 562-564 ◽  
pp. 1286-1291
Author(s):  
Xue Song Zhou ◽  
Yi Qi Liu ◽  
You Jie Ma ◽  
Si Jia Liu
Keyword(s):  
Linear Systems ◽  
Stability Criterion ◽  
Matrix Equation ◽  
Switched Systems ◽  
Norm Convergence ◽  
Convergence Radius ◽  
Switched Linear Systems ◽  
Balance Point ◽  
Convergence Process ◽  
Stable Linear

The stable linear switched systems will converge to the balance Point. If different switched laws be chosen, the convergence Process will not be the same, so there is an optimal switched law. The issues of optimal switched law based on norm, convergence radius, convergence distance and convergence direction are respectively studied, and the optimal switched law is confirmed by solution of matrix equation. All kinds of instance have been considered synthetically, the synthetic optimal switched law is given, by which an optimal status of system in convergence process is reflected roundly. By calculate and simulation of practice examples and the using process of stability criterion is realized distinctly.

scholarly journals Constructive Algebra Methods for the L2-Problem For Stable Linear Systems

1994 ◽  
Vol 27 (8) ◽  
pp. 185-190
Author(s):  
Bernard Hanzon ◽  
Jan M. Maciejowski
Keyword(s):  
Linear Systems ◽  
Constructive Algebra ◽  
Stable Linear

Positivity of descriptor linear systems with regular pencils

2012 ◽  
Vol 61 (1) ◽  
pp. 101-113 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Positive Systems ◽  
Electrical Circuits ◽  
Numerical Examples ◽  
Standard Linear ◽  
Descriptor Linear Systems ◽  
The Relationship ◽  
Equivalent Conditions ◽  
Time Linear

Positivity of descriptor linear systems with regular pencilsThe positivity of descriptor continuous-time and discrete-time linear systems with regular pencils are addressed. Such systems can be reduced to standard linear systems and can be decomposed into dynamical and static parts. Two definitions of the positive systems are proposed. It is shown that the definitions are not equivalent. Conditions for the positivity of the systems and the relationship between two classes of positive systems are established. The considerations are illustrated by examples of electrical circuits and numerical examples.

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