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