Analysis of piecewise constant delay systems via block-pulse functions

1981 ◽  
Vol 12 (5) ◽  
pp. 625-633 ◽  
Author(s):  
WEN-LIANG CHEN ◽  
BOR-SHINN JENG
Keyword(s):  
Delay Systems ◽  
Constant Delay ◽  
Piecewise Constant ◽  
Block Pulse Functions

scholarly journals Numerical Solution of Piecewise Constant Delay Systems Based on a Hybrid Framework

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
H. R. Marzban ◽  
S. Hajiabdolrahmani
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Operational Matrix ◽  
Delay Systems ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Constant Delay ◽  
Piecewise Constant ◽  
Delay Function ◽  
Delay Differential

An efficient numerical scheme for solving delay differential equations with a piecewise constant delay function is developed in this paper. The proposed approach is based on a hybrid of block-pulse functions and Taylor’s polynomials. The operational matrix of delay corresponding to the proposed hybrid functions is introduced. The sparsity of this matrix significantly reduces the computation time and memory requirement. The operational matrices of integration, delay, and product are employed to transform the problem under consideration into a system of algebraic equations. It is shown that the developed approach is also applicable to a special class of nonlinear piecewise constant delay differential equations. Several numerical experiments are examined to verify the validity and applicability of the presented technique.

scholarly journals Analysis of Linear Piecewise Constant Delay Systems Using a Hybrid Numerical Scheme

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
H. R. Marzban ◽  
S. M. Hoseini
Keyword(s):  
Numerical Scheme ◽  
Delay Systems ◽  
Computational Technique ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Constant Delay ◽  
Smooth Functions ◽  
Piecewise Constant ◽  
Delay Function ◽  
Linear Delay

An efficient computational technique for solving linear delay differential equations with a piecewise constant delay function is presented. The new approach is based on a hybrid of block-pulse functions and Legendre polynomials. A key feature of the proposed framework is the excellent representation of smooth and especially piecewise smooth functions. The operational matrices of delay, derivative, and product corresponding to the mentioned hybrid functions are implemented to transform the original problem into a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the proposed numerical scheme.

scholarly journals On time transformations for differential equations with state-dependent delay

2014 ◽  
Vol 12 (2) ◽  
Author(s):  
Alexander Rezounenko
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Asymptotic Properties ◽  
The State ◽  
Delay Systems ◽  
Constant Delay ◽  
Systems Of Differential Equations ◽  
State Dependent ◽  
State Dependent Delay ◽  
Time Transformations

AbstractSystems of differential equations with state-dependent delay are considered. The delay dynamically depends on the state, i.e. is governed by an additional differential equation. By applying the time transformations we arrive to constant delay systems and compare the asymptotic properties of the original and transformed systems.

A chain observer for nonlinear long constant delay systems: A matrix inequality approach

Automatica ◽  
2016 ◽  
Vol 65 ◽  
pp. 164-169 ◽  
Author(s):  
Alaleh Vafaei ◽  
Mohammad Javad Yazdanpanah
Keyword(s):  
Delay Systems ◽  
Matrix Inequality ◽  
Constant Delay ◽  
A Chain
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