Software for closed-form solutions of linear time-invariant differential systems

1986 ◽  
Vol 2 (3) ◽  
pp. 25-33 ◽  
Author(s):  
Mojtabaa Chinichiaan ◽  
Charles T. Fulton
Keyword(s):  
Closed Form ◽  
Linear Time ◽  
Differential Systems ◽  
Closed Form Solutions ◽  
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.

scholarly journals Temporal Variability in the Response of a Linear Time-Invariant Catchment System to a Non-Stationary Inflow Concentration Field

2020 ◽  
Vol 10 (15) ◽  
pp. 5356
Author(s):  
Ching-Min Chang ◽  
Kuo-Chen Ma ◽  
Mo-Hsiung Chuang
Keyword(s):  
Closed Form ◽  
Temporal Variability ◽  
Linear Time ◽  
Concentration Field ◽  
Surface Water Quality ◽  
Catchment Scale ◽  
Input Concentration ◽  
Linear Time Invariant ◽  
Linear Time Invariant System ◽  
Time Invariant

Predicting the effects of changes in dissolved input concentration on the variability of discharge concentration at the outlet of the catchment is essential to improve our ability to address the problem of surface water quality. The goal of this study is therefore dedicated to the stochastic quantification of temporal variability of concentration fields in outflow from a catchment system that exhibits linearity and time invariance. A convolution integral is used to determine the output of a linear time-invariant system from knowledge of the input and the transfer function. This work considers that the nonstationary input concentration time series of an inert solute to the catchment system can be characterized completely by the Langevin equation. The closed-form expressions for the variances of inflow and outflow concentrations at the catchment scale are derived using the Fourier–Stieltjes representation approach. The variance is viewed as an index of temporal variability. The closed-form expressions therefore allow to evaluate the impacts of the controlling parameters on the temporal variability of outflow concentration.

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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