This book introduces a new set of orthogonal hybrid functions (HF) which approximates time functions in a piecewise linear manner which is very suitable for practical applications. The book presents an analysis of different systems namely, time-invariant system, time-varying system, multi-delay systems---both homogeneous and non-homogeneous type- and the solutions are obtained in the form of discrete samples. The book also investigates system identification problems for many of the above systems. The book is spread over 15 chapters and contains 180 black and white figures, 18 colour figures, 85 tables and 56 illustrative examples. MATLAB codes for many such examples are included at the end of the book.

Key Features: The Book Covers recent results of the traditional block pulse and other functions related material Discusses ‘functions related to block pulse functions’ extensively along with their applications Contains analysis and identification of linear time-invariant systems, scaled system, and sampled-data system Presents an overview of piecewise constant orthogonal functions starting from Haar to sample-and-hold function Includes examples and MATLAB codes with supporting numerical exampless.

This book addresses a range of solutions and effective control techniques for Microbial Fuel Cells (MFCs), intended as a response to the increased energy consumption and wastewater production stemming from globalization. It describes the fundamentals of MFCs and control-oriented mathematical models, and provides detailed information on uncertain parameters. Various control techniques like robust control with LMI, adaptive backstepping control, and exact linearization control are developed for different mathematical models. In turn, the book elaborates on the basics of adaptive control, presenting several methods in detail. It also demonstrates how MFCs can be developed at the laboratory level, equipping readers to develop their own MFCs for experimental purposes. In closing, it develops a transfer function model for MFCs by combining a system identification technique and model reference adaptive control techniques. By addressing one of the most promising sources of clean and renewable energy, this book provides a viable solution for meeting the world’s increasing energy demands.

Orthogonal Functions may be divided into two classes. The class of continuous systems and the discontinuous class of piecewise constant systems. Problems arise because continuous systems form an unsatisfactory basis for the expansion of functions containing discontinuities whilst piecewise constant systems insert artificial discontinuities into all representations. Since these two classes of functions would be unsuccessful in coping with functions that possess both continuity and discontinuity we must look to General Hybrid Orthogonal Functions (GHOF) which have been shown to be the most appropriate in such situations. This book introduces the system of GHOF, discusses its properties, develops an operational algebra for the discretization of continuous dynamic systems on the system of GHOF and illustrates its use as a flexible and powerful framework of computational tools in a wide range of systems and control.

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