White Paper: Stability of Discrete Systems Controlled in the Presence of Intermittent Sensor Faults

This paper presents sufficient conditions for stability of unstable discrete time invariant models, stabilized by state feedback, when interrupted observations due to intermittent sensor faults occur. It is shown that the closed-loop system with feedback through a reconstructed signal, when, at least, one of the sensors is unavailable, remains stable, provided that the intervals of unavailability satisfy a certain time bound, even in the presence of state vanishing perturbations. The result is first proved for linear systems and then extended to a class of Hammerstein systems.

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In recent years, the mass advent of digital communication networks and systems has boosted the integration of teleoperationin feedback control systems. Applications like unmanned vehicles [1] or internet-based real time control [2]provide significant examples raising, in turn, new problems.This paper deals with one of such problems, if the communication channel through which feedback information passes is not completely reliable, sensors’ measurements may not be available to the controller during some intervals of time. In such a situation, one has to couple the controller with a block, hereafter called supervisor, which is able to discriminate between intervals of signal availability(availability time Tai ) and unavailability (unavailability time Tui+1 ), and to generate an estimate of the plant’s state during this Tui+1 intervals. Methods for detection and estimation for abruptly changing systems [3] can be applied in the problem considered here. For that purpose an algorithm based on Bayesian decision could be implemented, for example.

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