Modeling of variable coefficient Roesser model for systems described by second-order partial differential equation

C. W. Chen, Jason Sheng-Hon Tsai, L. S. Shieh

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

This paper addresses how a variable coefficient, two-dimensional (2D) multiple-input, multiple-output system described by second-order partial differential equations (PDEs) can be converted to a discrete variable coefficient Roesser model (RM). The following important question for its practical application is addressed: How does the choice of the finite difference operators for each differential operator and the respective integral intervals determine whether it is possible to arrive at a formulation according to the RM? This problem has not yet been addressed in generality. The results presented give a clear procedure to follow in the application of a finite difference discretization. The proposed prescription covers some important aspects, such as the state-space structure of variable coefficient difference equations, setting the states of the RM, and modeling of the RM, all of which are clearly interdependent. The proposed state-space modeling of a 2D system described by a PDE provides a powerful tool for analysis, design, and processing of variables and processes depending on two independent variables, one of which may be time. In particular, the model is very useful for 2D system control, such as observer design, optimal filter design, and state-feedback control methodologies presented in the literature.

Original languageEnglish
Pages (from-to)423-463
Number of pages41
JournalCircuits, Systems, and Signal Processing
Volume22
Issue number5
DOIs
Publication statusPublished - 2003 Jan 1

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Variable Coefficients
Second order differential equation
Partial differential equations
Partial differential equation
Modeling
2-D Systems
Finite Difference
State-space Modeling
Optimal Filter
Observer Design
Model
Multiple-input multiple-output (MIMO) Systems
State Feedback Control
Discrete Variables
Filter Design
Difference Operator
Difference equation
Difference equations
Differential operator
State feedback

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Applied Mathematics

Cite this

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Modeling of variable coefficient Roesser model for systems described by second-order partial differential equation. / Chen, C. W.; Tsai, Jason Sheng-Hon; Shieh, L. S.

In: Circuits, Systems, and Signal Processing, Vol. 22, No. 5, 01.01.2003, p. 423-463.

Research output: Contribution to journalArticle

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