scholarly journals Exponential Stability of Linear Discrete Systems with Variable Delays via Lyapunov Second Method

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Josef Diblík
Keyword(s):  
Exponential Stability ◽  
Lyapunov Functions ◽  
Lyapunov Equation ◽  
Discrete Systems ◽  
Type Estimate ◽  
System Of Difference Equations ◽  
Variable Delays ◽  
New Criteria ◽  
Lyapunov Second Method ◽  
Linear Discrete Systems

The paper investigates the exponential stability of a linear system of difference equations with variable delays xk+1=Axk+∑i=1sBikxk-mik, k=0,1,… , where s∈N, A is a constant square matrix, Bik are square matrices, mik∈N∪0, and mik≤m for an m∈N. New criteria for exponential stability are derived using the method of Lyapunov functions and formulated in terms of the norms of matrices of linear terms and matrices solving an auxiliary Lyapunov equation. An exponential-type estimate of the norm of solutions is given as well. The efficiency of the derived criteria is numerically demonstrated by examples and their relations to the well-known results are discussed.

scholarly journals Exponential Stability of Linear Discrete Systems with Multiple Delays

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
J. Baštinec ◽  
H. Demchenko ◽  
J. Diblík ◽  
D. Ya. Khusainov
Keyword(s):  
Linear System ◽  
Exponential Stability ◽  
Difference Equations ◽  
Lyapunov Method ◽  
Discrete Systems ◽  
Exponential Estimate ◽  
Multiple Delays ◽  
System Of Difference Equations ◽  
New Criterion ◽  
Linear Discrete Systems

The paper investigates the exponential stability and exponential estimate of the norms of solutions to a linear system of difference equations with multiple delays xk+1=Axk+∑i=1sBixk-mi, k=0,1,…, where s∈N, A and Bi are square matrices, and mi∈N. New criterion for exponential stability is proved by the Lyapunov method. An estimate of the norm of solutions is given as well and relations to the well-known results are discussed.

Exponential stability of linear discrete systems with delay

2018 ◽  
Author(s):  
Josef Diblík ◽  
Denys Ya. Khusainov ◽  
Miroslava Růžičková
Keyword(s):  
Exponential Stability ◽  
Discrete Systems ◽  
Linear Discrete Systems

Stability of linear discrete systems with variable delays

2018 ◽  
Author(s):  
Jaromír Baštinec ◽  
Josef Diblík ◽  
Denys Khusainov
Keyword(s):  
Discrete Systems ◽  
Variable Delays ◽  
Linear Discrete Systems

scholarly journals An analysis for a special class of solution of a Duffing system with variable delays

2021 ◽  
Vol 6 (10) ◽  
pp. 11187-11199
Author(s):  
Ramazan Yazgan ◽  
Keyword(s):  
Exponential Stability ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Equation System ◽  
Banach Fixed Point Theorem ◽  
Duffing System ◽  
Variable Delays ◽  
Globally Exponential Stability ◽  
Pseudo Almost Automorphic ◽  
Pseudo Almost Periodicity

<abstract> <p>In this study, we are concerned the existence of pseudo almost automorphic (PAA) solutions and globally exponential stability of a Duffing equation system with variable delays. Some differential inequalities and the well-known Banach fixed point theorem are used for the existence and uniqueness of PAA solutions. Also, with the help of Lyapunov functions, sufficient conditions are obtained for globally exponential stability of PAA solutions. Since the PAA is more general than the almost and pseudo almost periodicity, this work is new and complementary compared to previous studies. In addition, an example is given to show the correctness of our results.</p> </abstract>

A HYBRID IMPULSIVE AND SWITCHING CONTROL STRATEGY FOR SYNCHRONIZATION OF NONLINEAR SYSTEMS AND APPLICATION TO CHUA'S CHAOTIC CIRCUIT

2006 ◽  
Vol 16 (01) ◽  
pp. 229-238 ◽  
Author(s):  
ZHI-HONG GUAN ◽  
DAVID J. HILL ◽  
JING YAO
Keyword(s):  
Nonlinear Systems ◽  
Exponential Stability ◽  
Control Strategy ◽  
Lyapunov Functions ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Switching Control ◽  
Chaotic Circuit ◽  
Switching Control Strategy ◽  
New Criteria

In this paper, a new hybrid impulsive and switching control strategy for synchronization of nonlinear systems is developed. Using switched Lyapunov functions, several new criteria for global exponential stability of hybrid impulsive and switching nonlinear systems are established and, particularly, some simple sufficient conditions for driving the synchronization error to zero exponentially are proposed. As an application, Chua's chaotic circuit is investigated.

scholarly journals Exponential stability of perturbed linear discrete systems

2016 ◽  
Vol 2016 (1) ◽  
Author(s):  
Josef Diblík ◽  
Denys Y Khusainov ◽  
Jaromír Baštinec ◽  
Andrii S Sirenko
Keyword(s):  
Exponential Stability ◽  
Discrete Systems ◽  
Linear Discrete Systems
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