On nonuniform exponential stability for skew-evolution semiflows in Banach spaces

The paper considers some concepts of nonuniform asymptotic stability for skew-evolution semiflows in Banach spaces, which we have introduced in [Megan, M. and Stoica, C., Exponential instability of skew-evolution semiflows in Banach spaces, Stud. Univ. Babes-Bolyai Math., LIII (2008), No. 1, 17–24] and for which we present equivalent definitions, as well as integral characterizations in a nonuniform setting. Some examples are included to illustrate the results and to clarify the differences between the uniform and nonuniform cases.

Download Full-text

Real Integrability Conditions for the Nonuniform Exponential Stability of Evolution Families on Banach Spaces

Inequalities and Applications ◽

10.1007/978-3-7643-8773-0_4 ◽

2008 ◽

pp. 31-42 ◽

Cited By ~ 1

Author(s):

Constantin Buşe

Keyword(s):

Exponential Stability ◽

Banach Spaces ◽

Evolution Families ◽

Integrability Conditions ◽

Nonuniform Exponential Stability

Download Full-text

Connections between Hyers-Ulam stability and uniform exponential stability of discrete evolution families of bounded linear operators over Banach spaces

Advances in Difference Equations ◽

10.1186/s13662-016-0881-8 ◽

2016 ◽

Vol 2016 (1) ◽

Cited By ~ 18

Author(s):

Tongxing Li ◽

Akbar Zada

Keyword(s):

Exponential Stability ◽

Banach Spaces ◽

Linear Operators ◽

Ulam Stability ◽

Bounded Linear Operators ◽

Bounded Linear ◽

Uniform Exponential Stability ◽

Evolution Families

Download Full-text

Asymptotic stability versus exponential stability in linear volterra difference equations of convolution type

The Journal of Difference Equations and Applications ◽

10.1080/10236199608808074 ◽

1996 ◽

Vol 2 (4) ◽

pp. 401-410 ◽

Cited By ~ 44

Author(s):

Saber Elaydi ◽

Satoru Murakami

Keyword(s):

Asymptotic Stability ◽

Exponential Stability ◽

Difference Equations ◽

Convolution Type ◽

Volterra Difference Equations

Download Full-text

Recursive Lyapunov Functions

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.3153107 ◽

1989 ◽

Vol 111 (4) ◽

pp. 641-645 ◽

Cited By ~ 2

Author(s):

Andrzej Olas

Keyword(s):

Asymptotic Stability ◽

Lyapunov Function ◽

Exponential Stability ◽

Performance Measures ◽

Lyapunov Functions ◽

Stability Problem ◽

Autonomous Systems ◽

Sequence Of Functions

The paper presents the concept of recursive Lyapunov function. The concept is applied to investigation of asymptotic stability problem of autonomous systems. The sequence of functions {Uα(i)} and corresponding performance measures λ(i) are introduced. It is proven that λ(i+1) ≤ λ(i) and in most cases the inequality is a strong one. This fact leads to a concept of a recursive Lyapunov function. For the very important applications case of exponential stability the procedure is effective under very weak conditions imposed on the function V = U(0). The procedure may be particularly applicable for the systems dependent on parameters, when the Lyapunov function determined from one set of parameters may be employed at the first step of the procedure.

Download Full-text

Datko-Pazy conditions for nonuniform exponential stability

The Journal of Difference Equations and Applications ◽

10.1080/10236198.2017.1408609 ◽

2017 ◽

Vol 24 (3) ◽

pp. 344-357 ◽

Cited By ~ 8

Author(s):

Davor Dragičević

Keyword(s):

Exponential Stability ◽

Nonuniform Exponential Stability

Download Full-text

On uniform exponential stability for skew-evolution semiflows on Banach spaces

Nonlinear Analysis ◽

10.1016/j.na.2009.08.019 ◽

2010 ◽

Vol 72 (3-4) ◽

pp. 1305-1313 ◽

Cited By ~ 11

Author(s):

Codruţa Stoica ◽

Mihail Megan

Keyword(s):

Exponential Stability ◽

Banach Spaces ◽

Uniform Exponential Stability

Download Full-text

Global Stability of a Markovian Jumping Chaotic Financial System with Partially Unknown Transition Rates under Impulsive Control Involved in the Positive Interest Rate

Mathematics ◽

10.3390/math7070579 ◽

2019 ◽

Vol 7 (7) ◽

pp. 579 ◽

Cited By ~ 5

Author(s):

Ruofeng Rao

Keyword(s):

Interest Rate ◽

Asymptotic Stability ◽

Exponential Stability ◽

Equilibrium Point ◽

Impulsive Control ◽

Financial System ◽

Transition Rates ◽

Markovian Jumping ◽

Regional Control ◽

Globally Exponential Stability

The intrinsic instability of the financial system itself results in chaos and unpredictable economic behavior. To gain the globally asymptotic stability of the equilibrium point with a positive interest rate of the chaotic financial system, pulse control is sometimes very necessary and is employed in this paper to derive the globally exponential stability of financial system. It should be pointed out that the delayed feedback model brings an essential difficulty so that the regional control method has to be adopted. In this paper, the author firstly employs impulsive control, regional control, the Lyapunov function technique, and variational methods to derive the stochastically globally asymptotic stability criterion of the economic balance point with a positive interest rate for a delayed feedback financial system with Markovian jumping and partially unknown transition rates. Besides, the mathematical induction method and the proof by contradiction are applied synthetically to deduce the globally exponential stability of the equilibrium point with a positive interest rate for the impulsive financial system without time-delays. Moreover, numerical examples illustrate that under suitable data conditions on the two main criteria mentioned above, the interest rates are positive decimals when the financial system reaches stability, which means better economic significance.

Download Full-text