Approximate discretization of regular descriptor (singular) systems with impulsive mode

Descriptor systems can describe algebraic constraints and impulsive behaviour of systems and hence represent more general and broad category of complex dynamical systems. The impulsive behaviour of descriptor systems must be eliminated as it can cause degradation and saturation in performance or even can damage the system. To eliminate impulsive modes using discrete-time controllers, discrete-time models of descriptor systems are required. This paper deals with this problem and proposes a novel discretization technique for regular descriptor systems with impulsive mode when the input is applied through a zero-order-hold device. Using the Kronecker canonical form, the system model is decomposed into exponential, static and impulsive modes. Exact discrete-time models of exponential and static modes are obtained but an approximate discrete-time model for impulsive mode is proposed using limiting value functions because exact discretization is not possible as digital devices cannot realize infinite magnitude in zero time. An upper bound on error introduced by discretization is also derived. In addition, a simulation example is presented to show the efficacy of the proposed technique.