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.

This book deals with a new set of triangular orthogonal functions, which evolved from the set of well-known block pulse functions (BPF), a major member of the piecewise constant orthogonal function (PCOF) family. Unlike PCOF, providing staircase solutions, this new set of triangular functions provides piecewise linear solution with less mean integral squared error (MISE).

After introducing the rich background of PCOF family, which includes Walsh, block pulse and other related functions, fundamentals of the newly proposed set - such as basic properties, function approximation, integral operational metrics, etc. - are presented. This set has been used for integration of functions, analysis and synthesis of dynamic systems and solution of integral equations. The study ends with microprocessor based simulation of SISO control systems using sample-and-hold functions and Dirac delta functions.

This book details the designing of hybrid control strategies for practical systems containing time varying uncertainties, disturbances, nonlinearities, unknown parameters, unmodelled dynamics, delays, etc., concurrently. In this book, the advantages of different controllers will be brought together to produce superior control performance for the practical systems. Being aware of the advantages of adaptive controller to tackle unknown constant, time varying uncertainties and time varying disturbances, a variant of adaptive controller, namely L1 adaptive controller, is hybridized with other strategies. In this book, to facilitate optimal parameter setting of the basic L1 adaptive controller, stochastic optimization technique will be hybridized with it. The stability of the optimization technique along with the controller will be guaranteed analytically with the help of spectral radius convergence. The proposed method exhibits satisfactory exploration and exploitation capabilities. Again, this book will throw light on tackling nonlinearities along with uncertainties and disturbances by hybridizing fuzzy logic with L1 adaptive controller. The performances of the designed controllers will be compared with different control methodologies to validate their effectiveness. The overall stability of the nonlinear system with the designed controller will be guaranteed with the help of fuzzy Lyapunov function to retain the zonal behaviour of the system. This fuzzy PDC-L1 adaptive controller is efficient to tackle nonlinearities and at the same time cancels unknown constant, time varying uncertainties and time varying disturbances adequately. This book will also contain four simulation case studies to validate fruitfulness of the designed controllers. To demonstrate the superior control ability of these controllers in tackling practical system, three experimental case studies will also be provided.

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.