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.

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 Zero Controllability Criterion for Discrete Positive Systems with Multiple Delays on Both States and Inputs

2021 ◽  
Vol 2021 ◽  
pp. 1-5
Author(s):  
Mouhcine Naim
Keyword(s):  
Discrete Systems ◽  
Multiple Delays ◽  
Positive Systems ◽  
Linear Discrete Systems

Zero controllability criterion for positive linear discrete systems with multiple delays in both states and inputs is obtained and proved. An example is given to support our main result.

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
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