Necessary and sufficient numerical conditions for asymptotic stability of linear time-varying systems

2008 ◽  
Author(s):  
Germain Garcia ◽  
Pedro L. D. Peres ◽  
Sophie Tarbouriech
Keyword(s):  
Asymptotic Stability ◽  
Linear Time ◽  
Time Varying ◽  
Time Varying Systems ◽  
Necessary And Sufficient

Asymptotic Stability of Second-Order Linear Time-Varying Systems

2006 ◽  
Vol 29 (6) ◽  
pp. 1472-1476 ◽  
Author(s):  
Ryotaro Okano ◽  
Takashi Kida ◽  
Tomoyuki Nagashio
Keyword(s):  
Asymptotic Stability ◽  
Linear Time ◽  
Second Order ◽  
Time Varying ◽  
Order Linear ◽  
Time Varying Systems

scholarly journals On the Global Asymptotic Stability of Switched Linear Time-Varying Systems with Constant Point Delays

2008 ◽  
Vol 2008 ◽  
pp. 1-31 ◽  
Author(s):  
M. de la Sen ◽  
A. Ibeas
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Linear Time ◽  
Time Varying ◽  
System Matrix ◽  
Almost Everywhere ◽  
Time Varying Systems ◽  
The Matrix ◽  
Delayed System ◽  
Point Delays

This paper investigates the asymptotic stability of switched linear time-varying systems with constant point delays under not very stringent conditions on the matrix functions of parameters. Such conditions are their boundedness, the existence of bounded time derivatives almost everywhere, and small amplitudes of the appearing Dirac impulses where such derivatives do not exist. It is also assumed that the system matrix for zero delay is stable with some prescribed stability abscissa for all time in order to obtain sufficiency-type conditions of asymptotic stability dependent on the delay sizes. Alternatively, it is assumed that the auxiliary system matrix defined for all the delayed system matrices being zero is stable with prescribed stability abscissa for all time to obtain results for global asymptotic stability independent of the delays. A particular subset of the switching instants is the so-called set of reset instants where switching leads to the parameterization to reset to a value within a prescribed set.

scholarly journals Observability conditions of linear time-varying systems and its computational complexity aspects

2002 ◽  
Vol 8 (4-5) ◽  
pp. 439-449 ◽  
Author(s):  
Konstantin E. Starkov
Keyword(s):  
Computational Complexity ◽  
Analytic Function ◽  
Finite Number ◽  
Linear Time ◽  
Time Varying ◽  
Two Dimensional ◽  
Exponential Functions ◽  
Time Varying Systems ◽  
Necessary And Sufficient ◽  
Matrix Exponentials

We propose necessary and sufficient Observability conditions for linear time-varying systems with coefficients being time polynomials. These conditions are deduced from the Gabrielov–Khovansky theorem on multiplicity of a zero of a Noetherian function and the Wei–Norman formula for the representation of a solution of a linear time-varying system as a product of matrix exponentials. We define a Noetherian chain consisted of some finite number of usual exponentials corresponding to this system. Our results are formulated in terms of a Noetherian chain generated by these exponential functions and an upper bound of multiplicity of zero of one locally analytic function which is defined with help of the Wei–Norman formula. Relations with Observability conditions of bilinear systems are discussed. The case of two-dimensional systems is examined.

A numerical sufficiency test for the asymptotic stability of linear time-varying systems

Automatica ◽  
2007 ◽  
Vol 43 (4) ◽  
pp. 631-638 ◽  
Author(s):  
Ph. Mullhaupt ◽  
D. Buccieri ◽  
D. Bonvin
Keyword(s):  
Asymptotic Stability ◽  
Linear Time ◽  
Time Varying ◽  
Time Varying Systems

Asymptotic Stabilization of Fractional Permanent Magnet Synchronous Motor

2017 ◽  
Vol 13 (2) ◽  
Author(s):  
Yuxiang Guo ◽  
Baoli Ma
Keyword(s):  
Nonlinear Dynamics ◽  
Asymptotic Stability ◽  
Permanent Magnet ◽  
Linear Time ◽  
Permanent Magnet Synchronous Motor ◽  
Synchronous Motor ◽  
Time Varying ◽  
Linear Time Invariant ◽  
Time Varying Systems ◽  
The Stability

This paper is mainly concerned with asymptotic stability for a class of fractional-order (FO) nonlinear system with application to stabilization of a fractional permanent magnet synchronous motor (PMSM). First of all, we discuss the stability problem of a class of fractional time-varying systems with nonlinear dynamics. By employing Gronwall–Bellman's inequality, Laplace transform and its inverse transform, and estimate forms of Mittag–Leffler (ML) functions, when the FO belongs to the interval (0, 2), several stability criterions for fractional time-varying system described by Riemann–Liouville's definition is presented. Then, it is generalized to stabilize a FO nonlinear PMSM system. Furthermore, it should be emphasized here that the asymptotic stability and stabilization of Riemann–Liouville type FO linear time invariant system with nonlinear dynamics is proposed for the first time. Besides, some problems about the stability of fractional time-varying systems in existing literatures are pointed out. Finally, numerical simulations are given to show the validness and feasibleness of our obtained stability criterions.

Necessary and Sufficient Conditions for Assignability of the Lyapunov Spectrum of Discrete Linear Time-Varying Systems

2018 ◽  
Vol 63 (11) ◽  
pp. 3825-3837 ◽  
Author(s):  
Artur Babiarz ◽  
Irina Banshchikova ◽  
Adam Czornik ◽  
Evgenii K. Makarov ◽  
Michal Niezabitowski ◽  
...  
Keyword(s):  
Linear Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Lyapunov Spectrum ◽  
Time Varying ◽  
Time Varying Systems ◽  
Necessary And Sufficient
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