Book Description

In this book, we have illustrated the piece wise continuous orthogonal function, hybrid Function (an amalgamation of Sample and Hold function and Right hand triangular function) and presented an insightful review of the properties of hybrid function, for the readers. We have applied the hybrid function (HF) algorithm on approximating electrical circuit output, state-estimation of control system, solution of different practical system dened by fractional differential equation and Volterra, Fredholm and Hammerstein integral equation. Though HF does not possess proper orthogonality but the engineering problems we are dealing in this book are solved with a negligible error margin with HF approach. To device the control law for optimum performance of a control system we need to have the whole information on state vectors, but in reality most of the time, one or a few state vectors are unknown, to approximate these state vectors an observer is employed, we have employed a Luenberger observer alongside HFalgorithm to determinethe unknown state vector. Volterra,Fredholm, Hammerstein equations play an important role in electromagnetic, semiconductor physics, epidemiology, etc. Previously many complicated method were derived by researchers to deal with these classes of equation, but, in this book we propose a simple, straight-forward yet effective HF algorithm to yield numerical solution to these kinds of equations. Fractional calculus is the heart and soul of many bio-engineering models. Here we have chosen a few bio engineering fractional differential systems to estimate their characteristics via HF method and have drawn comparison with the actual ones. Numerical examples are illustrated throughout the book to help understand the readers and validate the HF algorithm. Here our aim is to present the HF method as an alternative to the known methods such as successive approximation method, Laplace method, Adomian method, etc. to solve problems regarding linear and non-linear system. The superiority of this method lies in its simplicity, given the fact, that all the integration and differentiation in HF domain gets transformed into simple matrix multiplication.