Minimal Root Sensitivity in Linear Systems

Skelton, Robert E.; Wagie, D.

doi:10.1016/s1474-6670(17)62422-4

Cited by 6 publications

(7 citation statements)

References 11 publications

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“…The deviation of each pole/zero is proportional to its sensitivity with respect to . The computation of pole sensitivity functions is well known and can be found in e.g., [12], [15], [16]. It is based on the following theorem.…”

Section: Preliminariesmentioning

confidence: 99%

“…Remark 2: These Frobenius norm based sensitivity measures were used in [8] and [16] and can be justified as follows. A commonly used assumption in FWL error analysis is that the perturbations on the elements of are independent and uniformly distributed random variables in the interval with some small constant, depending on the wordlength (see, e.g., [8], [12] and [18]).…”

Section: Preliminariesmentioning

confidence: 99%

“…Replacing in (10) with , where is given by (16), one can see that all realizations in the minimal zero sensitivity realization set have the same pole sensitivity measure. This is not the case for the optimal pole sensitivity realization set.…”

Section: Simultaneous Pole/zero Sensitivity Minimizationmentioning

confidence: 99%

“…Clearly, this conclusion falls short of generality. In [16], Skelton and Wagie concluded that the realizations whose matrix is normal have a minimal pole sensitivity, but the problem of how to transform a realization into an optimal one was not addressed. Gevers and Li obtained the same conclusion and a number of results in zero sensitivity [12].…”

Section: Introductionmentioning

confidence: 99%

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On pole and zero sensitivity of linear systems

1997

IEEE Trans. Circuits Syst. I

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The pole and zero sensitivity with respect to a realization of linear systems is investigated. It is shown that the pole and zero sensitivity measure depend strongly upon the realization chosen. The set of optimal similarity transformations that convert any realization into an optimal one is completely characterized in terms of minimizing pole and zero sensitivity measure, respectively. The pole and zero sensitivity simultaneous minimization problem is considered. The necessary and sufficient condition is given for the optimal zero sensitivity realizations with minimal pole sensitivity. An iterative algorithm is proposed to find the optimal realizations. A numerical example is given which confirms the theoretical results.

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Section: Preliminariesmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

Section: Simultaneous Pole/zero Sensitivity Minimizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On pole and zero sensitivity of linear systems

1997

IEEE Trans. Circuits Syst. I

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“…aAI''' = Re aAI''' = Re (a; )Aa;)" , (6.52) the norm of the modulus sensitivity matrix is (Pierre, C., 1989) then the eigenvectors at and a; are colinear: at = ai (Skelton, R.E., and Wagie, D.A., 1984). Near normal A implies minimal root sensitivity, but minimizing abnormality in combination with quadratic performance may unexpectedly cause increase of root sensitivity.…”

Section: Norm Of the Sensitivity Matricesmentioning

confidence: 99%

Uncertain Models and Robust Control

Weinmann¹

1991

312

126

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PrefaceControl system analysis and design are important fields in the engineering sciences. Process identification and optimum design have developed rapidly over the past decades and resulted in great engineering progress. However, many results have suffered from considerable dependence on uncertainties, mainly incorporated in the plant, in actuators and sensors, and released by other internal disturbances.More and more, methods tackling uncertainties form a central and important issue in designing feedback control systems. Choosing appropriate design methods, the influence of uncertainties on the closed-loop behaviour can be reduced to a large extent. Control systems particularly designed to manage uncertainties are called robust control systems. Robust control theory provides a design philosophy with respect to perturbed or uncertain parts of the system. This monograph is devoted to plants and their approximate models and to the discussion of their uncertainties. The thrust of the book is on systematic representation of methods for robust control.Most of the important areas of robust control are covered. The aim is to provide an introduction to the theory and methods of robust control system design, to present a coherent body of knowledge, to clarify and unify presentation, and to streamline derivations and proofs in the field of uncertainties and robust control. The book contains a thorough treatment of important material which is scattered throughout the literature.The primary goal of the text is to present significant derivations and proofs. As far as less significant proofs or lengthy derivations are concerned, only the results are outlined and the reader is referred to the literature relevant to this subject. In a few cases, some topics are set forth only as a suggestion for further reading.Some important problems treated in this book are:• How is uncertainty described and bounded when applying methods of differential equations, transfer functions or transfer matrices, state-space algorithms or some approximating calculus?• Which uncertainty or which perturbation in some special system description forces the system to instability? This question arises both for open-loop and for closed-loop systems.• Which kind of controller is able to tolerate maximum uncertainty?2In most cases stability robustness is applied but performance robustness is also a very important subject, e.g., determining the regions in the parameter space of controllers which place all the closed-loop eigenvalues into a desired region, thus satisfying the design specifications in the face of uncertain but bounded plant parameters.The book is intended specifically for practicing but mathematically inclined engineers, for postgraduate students and engineers on master's level. Moreover, the book is intended for those readers who wish to apply robust design principles and theories to real-life applications and problems.Emphasis is put on practical considerations and on applicability at the expense of extensive proofs and mathematical rigor.The ...

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Controller reduction by component cost analysis

Yousuff

Skelton²

1984

IEEE Trans. Automat. Contr.

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Minimal Root Sensitivity in Linear Systems

Cited by 6 publications

References 11 publications

On pole and zero sensitivity of linear systems

On pole and zero sensitivity of linear systems

Uncertain Models and Robust Control

Controller reduction by component cost analysis

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