On inconsistent initial conditions for linear time-invariant differential-algebraic equations

2002 ◽  
Vol 49 (11) ◽  
pp. 1646-1648 ◽  
Author(s):  
G. Reissig ◽  
H. Boche ◽  
P.I. Barton
Keyword(s):  
Initial Conditions ◽  
Linear Time ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Linear Time Invariant ◽  
Invariant Differential ◽  
Time Invariant

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.

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.

ODE observers for DAE systems

2018 ◽  
Vol 36 (4) ◽  
pp. 1375-1393 ◽  
Author(s):  
Thomas Berger ◽  
Timo Reis
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Linear Time ◽  
Observer Design ◽  
Simple Criterion ◽  
Linear Time Invariant ◽  
Ode System ◽  
Dae Systems ◽  
Invariant Differential ◽  
Time Invariant

Abstract We consider linear time-invariant differential-algebraic systems which are not necessarily regular. The following question is addressed: when does an (asymptotic) observer which is realized by an ordinary differential equation (ODE) system exist? In our main result we characterize the existence of such observers by means of a simple criterion on the system matrices. To be specific, we show that an ODE observer exists if, and only if, the completely controllable part of the system is impulse observable. Extending the observer design from earlier works we provide a procedure for the construction of (asymptotic) ODE observers.

scholarly journals Singular perturbation methods for a class of initial and boundary value problems in multi-parameter classical digital control systems

2004 ◽  
Vol 46 (1) ◽  
pp. 67-77 ◽  
Author(s):  
M. S. Krishnarayalu
Keyword(s):  
Boundary Value Problems ◽  
Digital Control ◽  
Perturbation Methods ◽  
Initial Conditions ◽  
Linear Time ◽  
Boundary Value ◽  
Linear Time Invariant ◽  
Digital Control Systems ◽  
Perturbation Parameters ◽  
Time Invariant

AbstractA stable linear time-invariant classical digital control system with several widely different small coefficients multiplying the lowest functions is considered. It is formulated as a multi-parameter singularly perturbed system. Perturbation methods are developed for both initial and boundary value problems based on asymptotic expansions of the perturbation parameters. The approximate solution consists of an outer solution and a number of boundary layer correction solutions equal to the number of initial conditions lost in the process of degeneration. An example is provided for illustration.

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