Analysis and synthesis of state models involving jump discontinuities in hybrid functions (HF) domain

Jump discontinuities in control systems pose difficulties in mathematical modeling. This paper uses a set of orthogonal hybrid functions (HF) for analysing and identifying control systems with jump discontinuities. But with traditional hybrid function theory, the results obtained are not quite satisfactory. To obtain a more accurate as well as reliable result, a modified version of the hybrid function set is attempted to design a new theory. With this new theory, jump functions are approximated in a better manner and subsequently these principles are applied for the analysis and synthesis of control systems described by their state models. Relevant examples are treated and results are found to be far more acceptable than those obtained using traditional hybrid functions.