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Analysis and Identification of Time-Invariant Systems, Time-Varying Systems, and Multi-Delay Systems using Orthogonal Hybrid Functions

Part of the Studies in Systems, Decision and Control Book Series (volume 46)

DOI: 10.1007/978-3-319-26684-8

ISBN: 978-3-319-26682-4

Publisher: Springer International Publishing - Springer Journals

Jan 6, 2016

1 - 10 of 15 Chapters

LitStream

Chapter 1Non-sinusoidal Orthogonal Functions in Systems and Control

Deb, Anish; Roychoudhury, Srimanti; Sarkar, Gautam

Pages: 1 –23

[This chapter discusses different types of non-sinusoidal orthogonal functionsnon-sinusoidal orthogonal functions such as Haar functions, Walsh functions, block pulse functions, sample-and-hold functions, triangular functions, non-optimal block pulse functions and a few others. It also discusses...
LitStream

Chapter 2The Hybrid Function (HF) and Its Properties

Deb, Anish; Roychoudhury, Srimanti; Sarkar, Gautam

Pages: 25 –48

[Starting with a brief review of block pulse functionsblock pulse functions (BPF), sample-and-hold functionssample-and-hold functions (SHF) and triangular functions (TF), this chapter presents the genesis of hybrid functions (HF) mathematically. Then different elementary properties and...
LitStream

Chapter 3Function Approximation via Hybrid Functions

Deb, Anish; Roychoudhury, Srimanti; Sarkar, Gautam

Pages: 49 –86

[In this chapter, square integrable time functions of Lebesgue measure are approximated via hybrid functions and such approximations are compared with similar approximations using BPF and Legendre polynomials. For handling discontinuous functions, a modified method of approximation is suggested...
LitStream

Chapter 4Integration and Differentiation Using HF Domain Operational Matrices

Deb, Anish; Roychoudhury, Srimanti; Sarkar, Gautam

Pages: 87 –114

[This chapter introduces the operational matrices for integration as well as differentiation. In such hybrid function domain integration or differentiation, the function to be integrated or differentiated is first expanded in hybrid function domain and then operated upon by some special matrices...
LitStream

Chapter 5One-Shot Operational Matrices for Integration

Deb, Anish; Roychoudhury, Srimanti; Sarkar, Gautam

Pages: 115 –140

[This chapter is devoted to develop the theory of one-shot operational matrices. These matrices are useful for multiple integration and, in general, are superior to repeated integration using the first order integration matrices. Theory of one-shot operational matrices is presented and the...
LitStream

Chapter 6Linear Differential Equations

Deb, Anish; Roychoudhury, Srimanti; Sarkar, Gautam

Pages: 141 –166

[This chapter is devoted to linear differential equationslinear differential equations. That is, it presents the solution of first order differential equations using both HF domain differentiation operational matrices and integration operational matrices. Higher order differential equations are...
LitStream

Chapter 7Convolution of Time Functions

Deb, Anish; Roychoudhury, Srimanti; Sarkar, Gautam

Pages: 167 –184

[In this chapter, theory of hybrid function domain convolutionconvolution technique is presented. First, the rules for convolution for sample-and-hold functions and triangular functions are derived. Then, these two component results are combined to get the rules for convolution in HF domain. This...
LitStream

Chapter 8Time Invariant System Analysis: State Space Approach

Deb, Anish; Roychoudhury, Srimanti; Sarkar, Gautam

Pages: 185 –220

[This chapter is devoted to time invariant system analysistime invariant system analysis using state space approach in hybrid function platform. Both homogeneous and non-homogeneous systems are treated along with numerical examples. States and outputs of the systems are solved. Also, a...
LitStream

Chapter 9Time Varying System Analysis: State Space Approach

Deb, Anish; Roychoudhury, Srimanti; Sarkar, Gautam

Pages: 221 –239

[In this chapter, time varying system analysistime varying system analysis is presented using state space approach in hybrid function domain. Both homogeneous and non-homogeneous systems are treated along with numerical examples. States and outputs of the systems are solved. Illustration has been...
LitStream

Chapter 10Multi-delay System Analysis: State Space Approach

Deb, Anish; Roychoudhury, Srimanti; Sarkar, Gautam

Pages: 241 –270

[This chapter is devoted to multi-delay systemmulti-delay system analysis using state space approach in hybrid function domain. First, the theory of HF domain approximation of functions with time delay is presented. This is followed by integration of functions with time delay. Then analysis of...

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