Bond Graph Representation of Linear Time-Varying Systems

2016 ◽  
Author(s):  
Gilberto González-A ◽  
Peter C Breedveld ◽  
Israel Nuñez
Keyword(s):  
Linear Time ◽  
Bond Graph ◽  
Graph Representation ◽  
Time Varying ◽  
Time Varying Systems

Controllability and observability of LTV systems -bond graph approach-

2018 ◽  
Vol 11 (03) ◽  
pp. 1850038 ◽  
Author(s):  
Abderrahim Frih ◽  
Zakaria Chalh ◽  
Mostafa Mrabti
Keyword(s):  
Linear Time ◽  
Algebraic Approach ◽  
Graph Model ◽  
Bond Graph ◽  
Graph Representation ◽  
Space Representation ◽  
State Space Representation ◽  
Time Varying Systems ◽  
Controllability And Observability

In this paper, a new methodology is proposed to determinate the controllability and the observability matrices of linear time varying systems modeled by bond graph. As the bond graph model can be viewed as a state space representation and as a module (algebraic approach), the determination of controllability and observability matrices is presented with the graphical approach. The equivalence between the two approaches (Graphic, Mathematical) is proposed and a graphical methodology is pointed out directly on the bond graph representation.

scholarly journals The VIT Transform Approach to Discrete-Time Signals and Linear Time-Varying Systems

Eng ◽  
2021 ◽  
Vol 2 (1) ◽  
pp. 99-125
Author(s):  
Edward W. Kamen
Keyword(s):  
Discrete Time ◽  
Initial Conditions ◽  
Linear Time ◽  
Order Term ◽  
Initial Time ◽  
Time Varying ◽  
Varying Coefficients ◽  
Time Signals ◽  
Time Varying Systems ◽  
Time Varying Coefficients

A transform approach based on a variable initial time (VIT) formulation is developed for discrete-time signals and linear time-varying discrete-time systems or digital filters. The VIT transform is a formal power series in z−1, which converts functions given by linear time-varying difference equations into left polynomial fractions with variable coefficients, and with initial conditions incorporated into the framework. It is shown that the transform satisfies a number of properties that are analogous to those of the ordinary z-transform, and that it is possible to do scaling of z−i by time functions, which results in left-fraction forms for the transform of a large class of functions including sinusoids with general time-varying amplitudes and frequencies. Using the extended right Euclidean algorithm in a skew polynomial ring with time-varying coefficients, it is shown that a sum of left polynomial fractions can be written as a single fraction, which results in linear time-varying recursions for the inverse transform of the combined fraction. The extraction of a first-order term from a given polynomial fraction is carried out in terms of the evaluation of zi at time functions. In the application to linear time-varying systems, it is proved that the VIT transform of the system output is equal to the product of the VIT transform of the input and the VIT transform of the unit-pulse response function. For systems given by a time-varying moving average or an autoregressive model, the transform framework is used to determine the steady-state output response resulting from various signal inputs such as the step and cosine functions.

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