Microprocessor and MATLAB based function approximation, integration and differentiation using orthogonal hybrid functions (HF)

The present work proposes a new set of hybrid functions (HF) which evolved from the synthesis of sample-and-hold functions (SHF) and triangular functions (TF). The former is efficient for analyzing control systems with sample-and-hold while triangular functions established their superiority in obtaining piecewise linear solution of various control problems. The HF set uses the attractive features of both SHF and TF for function approximation, function integration and function differentiation. Since the presented set works with samples, it has many advantages. The theoretical findings related to function approximation, integration and differentiation are supported by many examples. The results are compared with the actual solutions along with their respective microprocessor and MATLAB realizations using HF based algorithm.