scholarly journals Exponential Stability Criteria for Nonautonomous Difference Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Rigoberto Medina
Keyword(s):  
Exponential Stability ◽  
Linear Systems ◽  
Difference Equations ◽  
Linear Operators ◽  
Stability Criteria ◽  
Bounded Linear ◽  
Varying Coefficients ◽  
Nonautonomous Systems ◽  
Freezing Method ◽  
Difference Systems

The aim of this paper is to characterize the exponential stability of linear systems of difference equations with slowly varying coefficients. Our approach is based on the generalization of the freezing method for difference equations combined with new estimates for the norm of bounded linear operators. The main novelty of this work is that we use estimates for the absolute values of entries of a matrix-valued function, instead of bounds on its eigenvalues. By this method, new explicit stability criteria for linear nonautonomous systems are derived.

scholarly journals New Conditions for the Exponential Stability of Pseudolinear Difference Equations in Banach Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Rigoberto Medina
Keyword(s):  
Exponential Stability ◽  
Banach Spaces ◽  
Nonlinear Perturbations ◽  
Small Perturbations ◽  
Norm Estimates ◽  
Infinite Dimensional ◽  
Varying Coefficients ◽  
Freezing Method ◽  
Difference Systems ◽  
Combined Use

We study the local exponential stability of evolution difference systems with slowly varying coefficients and nonlinear perturbations. We establish the robustness of the exponential stability in infinite-dimensional Banach spaces, in the sense that the exponential stability for a given pseudolinear equation persists under sufficiently small perturbations. The main methodology is based on a combined use of new norm estimates for operator-valued functions with the “freezing” method.

scholarly journals On Uniform Exponential Stability and Exact Admissibility of Discrete Semigroups

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Aftab Khan ◽  
Gul Rahmat ◽  
Akbar Zada
Keyword(s):  
Banach Space ◽  
Exponential Stability ◽  
Complex Banach Space ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Uniform Exponential Stability ◽  
Discrete Semigroup ◽  
Exponentially Stable ◽  
Discrete Semigroups

We prove that a discrete semigroup𝕋={T(n):n∈ℤ+}of bounded linear operators acting on a complex Banach spaceXis uniformly exponentially stable if and only if, for eachx∈AP0(ℤ+,X), the sequencen↦∑k=0n‍T(n-k)x(k):ℤ+→Xbelongs toAP0(ℤ+,X). Similar results for periodic discrete evolution families are also stated.

New delay-range-dependent robust exponential stability criteria for uncertain linear systems with discrete interval and distributed time-varying delays and nonlinear perturbations

2015 ◽  
Vol 08 (03) ◽  
pp. 1550061
Author(s):  
Pornthip Somchai ◽  
Kanit Mukdasai
Keyword(s):  
Exponential Stability ◽  
Linear Systems ◽  
Time Varying ◽  
Nonlinear Perturbations ◽  
Stability Criteria ◽  
Robust Exponential Stability ◽  
Time Varying Delay ◽  
Discrete Interval ◽  
Uncertain Linear Systems ◽  
Varying Delay

In this paper, we investigate the problem of robust exponential stability analysis for uncertain linear systems with discrete interval time-varying delay, distributed time-varying delay and nonlinear perturbations. Based on constructing an augmented Lyapunov–Krasovskii functional with some parameter, decomposition technique of coefficient matrix, mixed model transformation with Leibniz–Newton formula and utilization of zero equations, new delay-range-dependent robust exponential stability criteria are derived in terms of linear matrix inequalities (LMIs). Numerical examples are given to show the superiority of our results to those in the literature.

scholarly journals New Delay-Range-Dependent Robust Exponential Stability Criteria of Uncertain Impulsive Switched Linear Systems with Mixed Interval Nondifferentiable Time-Varying Delays and Nonlinear Perturbations

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Piyapong Niamsup ◽  
Narongsak Yotha ◽  
Kanit Mukdasai
Keyword(s):  
Exponential Stability ◽  
Linear Systems ◽  
Continuous Functions ◽  
Linear Matrix ◽  
Time Varying ◽  
Nonlinear Perturbations ◽  
Stability Criteria ◽  
Parameter Uncertainties ◽  
Robust Exponential Stability ◽  
Switched Linear Systems

We investigate the problem of robust exponential stability analysis for uncertain impulsive switched linear systems with time-varying delays and nonlinear perturbations. The time delays are continuous functions belonging to the given interval delays, which mean that the lower and upper bounds for the time-varying delays are available, but the delay functions are not necessary to be differentiable. The uncertainties under consideration are nonlinear time-varying parameter uncertainties and norm-bounded uncertainties, respectively. Based on the combination of mixed model transformation, Halanay inequality, utilization of zero equations, decomposition technique of coefficient matrices, and a common Lyapunov functional, new delay-range-dependent robust exponential stability criteria are established for the systems in terms of linear matrix inequalities (LMIs). A numerical example is presented to illustrate the effectiveness of the proposed method.

EEFFECTIVE CRITERIA OF EXPONENTIAL STABILITY OF AUTONOMOUS DIFFERENCE EQUATIONS

2018 ◽  
pp. 402-414
Author(s):  
Aleksandr Andreyevich Kandakov ◽  
Kirill Mikhaylovich Chudinov
Keyword(s):  
Exponential Stability ◽  
Vector Function ◽  
Difference Equations ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Analytic Form ◽  
Stability Criteria ◽  
Three Dimensional Space

We obtain stability criteria for several classes of linear autonomous difference equations. The criteria are expressed in explisit analytic form, as well as in the form of belonging values of a vector function of the equation parameters to a domain in three-dimensional space.

scholarly journals Exponential Stability and Availability Analysis of a Complex Standby System

2014 ◽  
Vol 2 (3) ◽  
pp. 279-288 ◽  
Author(s):  
Chunli Wang ◽  
Mingyan Teng ◽  
Fu Zheng
Keyword(s):  
Exponential Stability ◽  
Semigroup Theory ◽  
Steady State Solution ◽  
Linear Operators ◽  
Well Posedness ◽  
Redundant System ◽  
Bounded Linear ◽  
Reliability Indices ◽  
Availability Analysis ◽  
System Operator

Abstract In this paper, we first investigate the solution of the two correlated units redundant system with two types of failure. By using the method of functional analysis, especially, the c0 semigroup theory of bounded linear operators on Banach space, we prove the well-posedness and the existence of positive solution of the system. By analyzing the spectra distribution of the system operator, we prove that the dynamic solution of the system asymptotically converges to the nonnegative steady-state solution which is the eigenfunction corresponding to eigenvalue 0 of the system operator. Furthermore, we discuss the exponential stability of the system. Finally, we analyze the reliability the system with the help of our main results and present some reliability indices of the system at the end of the paper.

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