Abstract
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.
Highlights
In recent years, the mass advent of digital communication networks and systems has boosted the integration of teleoperation in feedback control systems
The system with initial condition x(0) = x0 is globally uniformly stable provided that the total unavailability time Tu, up to discrete time k inside the unavailability interval Tui+1, satisfies the bound log log M1 β + α·σδA
The paper presents and proves sufficient conditions that allow a discrete time analysis of sensor unavailability intervals, bounding these intervals in order to state that the unstable open-loop plant represented in Figure 1, when controlled in closed-loop, is globally uniformly exponentially stable
Summary
The mass advent of digital communication networks and systems has boosted the integration of teleoperation in feedback control systems. In [11] the artifacts in the neuromuscular blockade level measurement in patients subject to general anaesthesia are modeled as sensor faults The occurrence of these faults is detected with a Bayesian algorithm and, during the periods of unavailability of the signal, the feedback controller is fed with an estimate generated by a model. It is shown, throughout the paper, that with the above described scheme, the controlled open-loop unstable plant will be stable (in some sense, to be defined later) if the time. Appendix A.1 gives a full proof of Theorem 1 and Corollaries 1 and 2, and Appendix A.2 gives a full proof of Theorem 2 and Corollaries 3 and 4
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