scholarly journals Necessary and Sufficient Conditions on the Exponential Stability of Positive Hyperbolic Systems

2017 ◽  
Vol 62 (7) ◽  
pp. 3610-3617 ◽  
Author(s):  
Liguo Zhang ◽  
Christophe Prieur
Keyword(s):  
Exponential Stability ◽  
Hyperbolic Systems ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient

scholarly journals Stability of arbitrarily switched discrete-time linear singular systems of index-1

2018 ◽  
Vol 34 (4) ◽  
Author(s):  
Pham Thi Linh
Keyword(s):  
Exponential Stability ◽  
Discrete Time ◽  
Switched Systems ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Positive Switched Systems ◽  
Necessary And Sufficient ◽  
Time Linear

In this paper, the index-1 notion for arbitrarily switched discrete-time linear singular systems (SDLS) has been introduced. Based on the Bohl exponents of SDLS as well as properties of associated positive switched systems, some necessary and sufficient conditions have been established for exponential stability.

scholarly journals Integral Characterizations for Uniform Stability with Growth Rates in Banach Spaces

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 235
Author(s):  
Rovana Boruga(Toma) ◽  
Mihail Megan ◽  
Daniela Maria-Magdalena Toth
Keyword(s):  
Exponential Stability ◽  
Banach Spaces ◽  
Growth Rates ◽  
Evolution Operator ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Uniform Stability ◽  
Polynomial Stability ◽  
Uniform Exponential Stability ◽  
Necessary And Sufficient

The aim of this paper is to present some integral characterizations for the concept of uniform stability with growth rates in Banach spaces. In this sense, we prove necessary and sufficient conditions (of Barbashin and Datko type) for an evolution operator to be uniform h- stable. As particular cases of this notion, we obtain four characterizations for uniform exponential stability and two characterizations for uniform polynomial stability.

On the Exponential Stability of the Singular Distributed Parameter Systems

2015 ◽  
Vol 719-720 ◽  
pp. 496-503
Author(s):  
Zhao Qiang Ge
Keyword(s):  
Hilbert Space ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Distributed Parameter Systems ◽  
Necessary And Sufficient Conditions ◽  
Distributed Parameter ◽  
Necessary And Sufficient

Exponential stability for the singular distributed parameter systems is discussed in the light of the theory of GE0-semigroup in Hilbert space. The necessary and sufficient conditions concerning the exponential stability are given.

Simple algebraic necessary and sufficient conditions for Lyapunov stability of a Chen system and their applications

2017 ◽  
Vol 40 (7) ◽  
pp. 2200-2210 ◽  
Author(s):  
Guopeng Zhou ◽  
Xiaoxin Liao ◽  
Bingji Xu ◽  
Pei Yu ◽  
Guanrong Chen
Keyword(s):  
Asymptotic Stability ◽  
Exponential Stability ◽  
Lyapunov Stability ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Linear Feedback ◽  
Chen System ◽  
Local Asymptotic Stability ◽  
Positive Elements ◽  
Necessary And Sufficient

In this paper, we study the Lyapunov stability problem of a Chen chaotic system. Because of the positive elements of the main diagonal of a linearized Chen system, compared to the coefficient of a linearized Lorenz system which are all negative, it is more difficult to deal with the stability analysis. Since it has the properties of invariance and symmetry, different Lyapunov functions in different regions are constructed to solve stability problems with geometric and algebraic methods. Then, simple algebraic necessary and sufficient conditions of global exponential stability, global asymptotic stability and global instability of equilibrium [Formula: see text] are proposed. We obtain the relevant expression of corresponding parameters for local exponential stability, local asymptotic stability and local instability of equilibria [Formula: see text]. Furthermore, the smallest conservative linear feedback controllers are used to globally exponentially stabilize equilibria.

Sign in / Sign up

Export Citation Format

Share Document