Solution of state-space equations via block-pulse functions

A recursive algorithm is developed for the piecewise-constant solution of dynamic equations via block-pulse functions φj(t),where j=1,2,...,m. For 1≤j≤m (where j and m are integers) and final timeT, each block-pulse function φj(t) is defined by φj(t)=1 for (j−1)T/m≤t<j T/m and φj(t)=1otherwise. Compared with Walsh function approaches, the proposed method is simpler to compute, is more suitable for computer programming, and provides the same accuracy. Also, a discrete-time solution is derived for a zero-input state equation.