Abstract
Starting with a brief review of block pulse functions (BPF), sample-and-hold functions (SHF) and triangular functions (TF), this chapter presents the genesis of hybrid functions (HF) mathematically. Then different elementary properties and operational rules of HF are discussed. The chapter ends with a qualitative comparison of BPF, SHF, TF and HF.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Sansone, G.: Orthogonal functions. Interscience, New York (1959)
Deb, A., Sarkar, G., Bhattacharjee, M., Sen, S.K.: A new set of piecewise constant orthogonal functions for the analysis of linear SISO systems with sample-and-hold. J. Franklin Inst. 335B(2), 333–358 (1998)
Deb, A., Sarkar, G., Senupta, A.: Triangular orthogonal functions for the analysis of continuous time systems. Anthem Press, London (2011)
Deb, A., Dasgupta, A., Sarkar, G.: A complementary pair of orthogonal triangular function sets and its application to the analysis of dynamic systems. J. Franklin Inst. 343(1), 1–26 (2006)
Rao, G.P.: Piecewise constant orthogonal functions and their applications in systems and control, LNC1S, vol. 55. Springer, Berlin (1983)
Jiang, J.H., Schaufelberger, W.: Block pulse functions and their application in control system, LNCIS, vol. 179. Springer, Berlin (1992)
Biswas, A.: Analysis and synthesis of continuous control systems using a set of orthogonal hybrid functions. Doctoral dissertation, University of Calcutta (2015)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Deb, A., Roychoudhury, S., Sarkar, G. (2016). The Hybrid Function (HF) and Its Properties. In: Analysis and Identification of Time-Invariant Systems, Time-Varying Systems, and Multi-Delay Systems using Orthogonal Hybrid Functions. Studies in Systems, Decision and Control, vol 46. Springer, Cham. https://doi.org/10.1007/978-3-319-26684-8_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-26684-8_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-26682-4
Online ISBN: 978-3-319-26684-8
eBook Packages: EngineeringEngineering (R0)