Analysis of linear discrete SISO control systems via a set of delta functions

The paper presents a computational technique through operational matrices using a set of mutually disjoint delta functions (DF) for the analysis of linear discrete control systems. Following a brief review of the well known block pulse functions (BPF), a new set of delta functions is viewed in the same light. This set is used to develop operational transfer functions in the delta function domain (DOTF) and employed for discrete system analysis which results in the same accuracy as the conventional z-transform method. The presented technique uses simple matrix manipulations and is able to do away with laborious and involved algebraic steps, including inverse transformation, associated with the z-transform analysis without losing accuracy. Also, the accuracy of sample values of the output does not depend upon m (or the sampling interval h). A few linear discrete SISO control systems, open loop as well as closed loop, having different typical plant transfer functions, are analysed as illustrative examples.