Regularization of linear time-invariant differential–algebraic systems

2015 ◽  
Vol 78 ◽  
pp. 40-46 ◽  
Author(s):  
Thomas Berger ◽  
Timo Reis
Keyword(s):  
Linear Time ◽  
Algebraic Systems ◽  
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.

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.

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