scholarly journals Stability of Time Varying Systems

1995 ◽  
Author(s):  
Fritz Colonius ◽  
Wolfgang Kliemann
Keyword(s):  
Linear Time ◽  
Hyperbolic Systems ◽  
Type Theorem ◽  
Time Varying ◽  
Time Varying Systems ◽  
Stable Manifold Theorem ◽  
The Stability ◽  
Stability Type ◽  
Stability Radii

Abstract The stability behavior of time varying systems can be studied using the concept of Lyapunov exponents and their corresponding Lyapunov subspaces. For linear time varying systems the entire Lyapunov spectrum can be approximated by the Floquet exponents of periodic systems. This leads to a variety of stability results, including the characterization of stability radii. Furthermore, a structural stability type theorem shows that stability features of time varying hyperbolic systems persist under small perturbations. For nonlinear time varying systems a stable manifold theorem allows us to interpret the linear results for the nonlinear system locally around an equilibrium point.

A Combined Time-Frequency Condition for Stability of Time-Varying Systems With One Nonlinearity

1971 ◽  
Vol 93 (4) ◽  
pp. 261-267 ◽  
Author(s):  
R. E. Blodgett ◽  
K. P. Young
Keyword(s):  
Stability Condition ◽  
Linear Time ◽  
Phase Variable ◽  
Time Varying ◽  
Asymptotically Stable ◽  
Frequency Condition ◽  
Time Frequency ◽  
Time Varying Systems ◽  
The Stability ◽  
Limiting Case

A means is presented for determining stability of linear time-varying systems with one feedback nonlinearity. The stability condition involves the minimization of certain time functions of the system coefficients as well as the imaginary axis behavior of a polynomial. It is required that the equation of the linear time-varying system be asymptotically stable and be in phase variable form. The nonlinearity is restricted to lie in a sector. For the limiting case of an autonomous linear system the criterion reduces to the Popov stability condition in certain cases.

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.

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