Generalized weighting function and restricted stability of a linear pulse-modulated error feedback system

A generalized weighting function is obtained for a linear feedback system with a pulse-modulated error signal. This is expressed in the form of a matrix operator acting on an input vector, the components of which are the first R − 1 derivatives of the input, where R is the order of the unmodulated closed-loop system. In addition, since the system operator takes the form of a finite dimensional matrix, it has been possible to make and realize more stringent conditions on the transient stability; namely, a preassigned bounded output after a preassigned time. Although the solution has been obtained generally for non-uniform pulsing, the latter stability investigation has been made only for the uniform case.