Book contents
- Frontmatter
- Contents
- Preface
- Chapter 1 Walsh, Block Pulse, and Related Orthogonal Functions in Systems and Control
- Chapter 2 A Newly Proposed Triangular Function Set and Its Properties
- Chapter 3 Function Approximation via Triangular Function Sets and Operational Matrices in Triangular Function Domain
- Chapter 4 Analysis of Dynamic Systems via State Space Approach
- Chapter 5 Convolution Process in Triangular Function Domain and Its Use in SISO Control System Analysis
- Chapter 6 Identification of SISO Control Systems via State Space Approach
- Chapter 7 Solution of Integral Equations via Triangular Functions
- Chapter 8 Microprocessor Based Simulation of Control Systems Using Orthogonal Functions
- Index
Chapter 7 - Solution of Integral Equations via Triangular Functions
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- Chapter 1 Walsh, Block Pulse, and Related Orthogonal Functions in Systems and Control
- Chapter 2 A Newly Proposed Triangular Function Set and Its Properties
- Chapter 3 Function Approximation via Triangular Function Sets and Operational Matrices in Triangular Function Domain
- Chapter 4 Analysis of Dynamic Systems via State Space Approach
- Chapter 5 Convolution Process in Triangular Function Domain and Its Use in SISO Control System Analysis
- Chapter 6 Identification of SISO Control Systems via State Space Approach
- Chapter 7 Solution of Integral Equations via Triangular Functions
- Chapter 8 Microprocessor Based Simulation of Control Systems Using Orthogonal Functions
- Index
Summary
In this chapter, efforts have been made to solve integral equations [1] using orthogonal triangular function (TF) sets. It is well known that, in control system analysis and synthesis, integral equations play an important role and often the control problem surmises to solving one or several integral equations. The proposed TFs, when used in a fashion similar to that of block pulse functions (BPF) [2,3], yield a piecewise linear solution of dynamic systems with less integral squared error (ISE).
The main objectives of the present work are:
(i) To solve Fredholm integral equation of the second kind [1] via TFs and compare the results with its BPF domain solution.
(ii) To solve Volterra integral equation of the second kind [1] via TFs and compare the results with its BPF domain solution.
The theory of the proposed TF method has been developed and then supported by several examples. Results are also compared with BPF domain solution with respect to ISE.
Solution of integral equations was of interest to the scientific community that is apparent from the year of publication of Ref. 1. With the advent of Walsh [4], block pulse [2,3], and related functions, interest of the researchers took a new turn and they thrived for finding out techniques that were computationally more attractive using new family of orthogonal functions.
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- Publisher: Anthem PressPrint publication year: 2011