scholarly journals Stability and Robust Stability of Linear Time-Invariant Delay Differential-Algebraic Equations

2013 ◽  
Vol 34 (4) ◽  
pp. 1631-1654 ◽  
Author(s):  
Nguyen Huu Du ◽  
Vu Hoang Linh ◽  
Volker Mehrmann ◽  
Do Duc Thuan
Keyword(s):  
Robust Stability ◽  
Linear Time ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Linear Time Invariant ◽  
Delay Differential ◽  
Time Invariant

Decentralized time-delay controller design for systems described by delay differential-algebraic equations

2021 ◽  
pp. 014233122110159
Author(s):  
H. Ersin Erol ◽  
Altuğ İftar
Keyword(s):  
Time Delay ◽  
Time Delays ◽  
Controller Design ◽  
Linear Time ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Design Algorithm ◽  
Linear Time Invariant ◽  
Delay Differential ◽  
Time Invariant

This paper presents a complete approach for designing stabilizing linear time-invariant decentralized finite-dimensional or retarded time-delay output feedback controllers for linear time-invariant systems of delay differential-algebraic equations. The proposed approach is based on the sequential design of the local controllers by using a centralized controller design algorithm. In this sequential design approach, the local controller to be designed at each step is determined depending on the mobility of the rightmost modes with respect to the controllers that have not yet been designed and closed with the system. Since no predefined sequence is followed, a sequence that can target the least effort and dimension for each agent can be aimed. Also, in the proposed approach, a base controller effort can be targeted for each control agent, so that the effort required to stabilize the system can be distributed among the local controllers. In the centralized controller design algorithm used for the design of each local controller, the parameters of the controllers are changed stepwise in a quasi-continuous way to shift the targeted rightmost modes towards the stable area. For a time-delay controller, the desired mode placement can be achieved by applying small changes stepwise to the elements of the matrices and the time-delays of the controller while time-delays remain always non-negative. The effect of small perturbations on the time-delays in the open-loop system or to be added by the controller to be designed is taken into account to ensure some degree of robustness against all possible perturbations on the delays. The effectiveness of the proposed design approach is demonstrated by a numerical example.

scholarly journals Differential-algebraic systems are generically controllable and stabilizable

2021 ◽  
Author(s):  
Achim Ilchmann ◽  
Jonas Kirchhoff
Keyword(s):  
Algebraic Geometry ◽  
Linear Time ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Algebraic Systems ◽  
Linear Time Invariant ◽  
Survey Article ◽  
Link Type ◽  
Invariant Differential ◽  
Time Invariant

AbstractWe investigate genericity of various controllability and stabilizability concepts of linear, time-invariant differential-algebraic systems. Based on well-known algebraic characterizations of these concepts (see the survey article by Berger and Reis (in: Ilchmann A, Reis T (eds) Surveys in differential-algebraic equations I, Differential-Algebraic Equations Forum, Springer, Berlin, pp 1–61. 10.1007/978-3-642-34928-7_1)), we use tools from algebraic geometry to characterize genericity of controllability and stabilizability in terms of matrix formats.

scholarly journals On the Stability Analysis of Delay Differential-Algebraic Equations

2018 ◽  
Vol 34 (2) ◽  
Author(s):  
Phi Ha
Keyword(s):  
Stability Analysis ◽  
Exponential Stability ◽  
Linear Time ◽  
Differential Algebraic Equations ◽  
Spectral Condition ◽  
Algebraic Equations ◽  
Linear Time Invariant ◽  
Stability Of Dynamical Systems ◽  
The Stability ◽  
Delay Differential

The stability analysis of linear time invariant delay differentialalgebraic equations (DDAEs) is analyzed. Examples are delivered to demonstrate that the eigenvalue-based approach to analyze the exponential stability of dynamical systems is not valid for an arbitrarily high index system, and hence, a new concept of weakly exponential stability (w.e.s) is proposed. Then, we characterize the w.e.s in term of a spectral condition for some special classes of DDAEs.

Parameter Estimation of Delay Systems Via Block Pulse Functions

1980 ◽  
Vol 102 (3) ◽  
pp. 159-162 ◽  
Author(s):  
Yen-Ping Shin ◽  
Chyi Hwang ◽  
Wei-Kong Chia
Keyword(s):  
Linear Time ◽  
Delay Systems ◽  
Algebraic Equations ◽  
Unknown Parameters ◽  
Linear Time Invariant ◽  
Least Squares Estimate ◽  
Block Pulse Functions ◽  
Linear Algebraic Equations ◽  
Delay Differential ◽  
Time Invariant

Linear time-invariant delay-differential equation systems are approximately represented by a set of linear algebraic equations with the block pulse functions. A least squares estimate is then used to determine the unknown parameters. Examples with satisfactory results are given.

scholarly journals Robust stability of positive linear time delay systems under time-varying perturbations

2015 ◽  
Vol 63 (4) ◽  
pp. 947-954
Author(s):  
P.H.A. Ngoc ◽  
C.T. Tinh
Keyword(s):  
Time Delay ◽  
Robust Stability ◽  
Linear Time ◽  
Delay Systems ◽  
Time Varying ◽  
Linear Time Invariant ◽  
Novel Approach ◽  
Delay Differential Systems ◽  
Delay Differential ◽  
Time Invariant

Abstract By a novel approach, we get explicit robust stability bounds for positive linear time-invariant time delay differential systems subject to time-varying structured perturbations or non-linear time-varying perturbations. Some examples are given to illustrate the obtained results. To the best of our knowledge, the results of this paper are new.

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