Exact Discrete-Time Model of a Time-Invariant System with Variable Sampling Periods

Noriyuki Hori, Hua-Feng Chen, and Alain C. Rabbath

Keywords

Variable sampling period, Exact discretetime model, Discretization, Digital statefeedback control

Abstract

An exact discretization method is presented for a linear time-invariant continuous-time system expressed in state-space form, where the sampling period may be varying. The resulting discrete-time model is linear but time-varying. This model is on-line computable when the system update is event-triggered or when the changes in sampling period occurs in a known manner, such as in repetitive or time-programmed control where the input profile is pre-designed or at least the subsequent sampling period is known. The sensitivity of the discrete-time model to uncertainty in the sampling period is shown to approach zero as this period approaches zero. As an application of the proposed model, digital state-feedback regulation is considered, where the feedback gain is determined to achieve exactly analog state-feedback regulation at all sampling instants. The technique developed for linear system can also be applied to some nonlinear systems that are linearizable exactly using variable transformations, such as a logistic system.

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