Orthogonal Functions and Their Properties
In this chapter a brief discussion on the history of OFs, their classification and their developments is given. The useful properties of BPFs and SLPs are given in detail. Lastly, the rationale for choosing BPFs and SLPs among all OFs, for the study of state estimation and optimal control problems, is stated.
The LPs, originated from determining the force of attraction exerted by solids of revolution [5], and their orthogonal properties were established by Adrian Marie Legendre (1752–1833) during 1784–1790. In 1807, Joseph Fourier (1768–1830), while solving partial differential equations encountered in connection with conduction of heat in a rod, discovered that the solution ...
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