On implementing passivity in discrete linear systems

Recent publications have shown that under some conditions continuous linear time-invariant systems become strictly positive real with constant feedback. This paper expands the applicability of this result to discrete linear systems. The paper shows the sufficient conditions that allow a discrete system to become stable and strictly passive via static (constant or nonstationary) output feedback. However, as the passivity conditions require a direct input-output connection that ends in an algebraic loop that includes the adaptive or nonlinear controller, they have been considered to be impossible to implement in realistic discrete-time systems. Therefore, this paper also finally solves the apparently inherent algebraic loop, thus allowing satisfaction of the passivity condition and implementation of adaptive and nonlinear control techniques in discrete-time positive real systems.