Some frequency-domain approaches to the model reduction of delay systems

The expanding integration of control and communication networks in recent years has generated an increasing interest in control problems with feedback over a communication channel. Significant research activity has concentrated on stabilisation in face of channel effects such as quantisation and data-rate limits. In a recent paper, the authors have studied the problem of feedback stabilisation over a communication channel with a constraint on the admissible signal-to-noise ratio (SNR). It has been shown therein that for a delay-free, linear time-invariant feedback loop, a SNR constraint in the feedback channel imposes fundamental limitations in the ability to achieve closed-loop stability. The present paper extends these results by introducing a time-delay in the loop, and shows that the lowest SNR required for closed-loop stability increases by a factor that may grow exponentially with the time-delay and the unstable open loop poles of the system. This result contributes to the quantification of performance tradeoffs in integrated control and communication environments.

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“…Namely, by using the Padé approximant (e.g., Partington, 2004) (n−k )!k ! is the binomial coefficient, we approximate G(s) in (7) by…”

Section: Numerical Computation Via Padé Approximantsmentioning

confidence: 99%

Effects of Time Delay on Feedback Stabilisation Over Signal-to-Noise Ratio Constrained Channels

Braslavsky

Middleton

Freudenberg

2005

IFAC Proceedings Volumes

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“…The controller we construct for P is distributed. To obtain an implementable finite dimensional controller, we have to approximate the controller; see, e.g., [29]- [31] and references therein.…”

Section: Examplementioning

confidence: 99%

Sensitivity Reduction by Strongly Stabilizing Controllers for MIMO Distributed Parameter Systems

Wakaiki

Yamämoto

Özbay

2012

IEEE Trans. Automat. Contr.

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Abstract-This note investigates a sensitivity reduction problem by stable stabilizing controllers for a linear time-invariant multi-input multioutput distributed parameter system. The plant we consider has finitely many unstable zeros, which are simple and blocking, but can possess infinitely many unstable poles. We obtain a necessary condition and a sufficient condition for the solvability of the problem, using the matrix Nevanlinna-Pick interpolation with boundary conditions. We also develop a necessary and sufficient condition for the solvability of the interpolation problem, and show an algorithm to obtain the solutions. Our method to solve the interpolation problem is based on the Schur-Nevanlinna algorithm.

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“…Below we outline some ideas used to answer these questions. For a more detailed and rigorous discussion and additional references the reader is referred to the survey paper [7].…”

Section: Rational Approximations Of Delay Systemsmentioning

confidence: 99%