Robust Control: The Parametric Approach

Bhattacharyya, S.P.; Chapellat, H.; Keel, L.H.

doi:10.1016/b978-0-08-042230-5.50016-5

Cited by 833 publications

(492 citation statements)

References 8 publications

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“…It follows from the above considerations and the fact that the positive interval system (36) is robustly stable if and only if the positive system (38) is asymptotically stable [28].…”

Section: Theoremmentioning

confidence: 93%

Robust stability of positive discrete-time linear systems of fractional order

Busłowicz¹

2010

Bulletin of the Polish Academy of Sciences: Technical Sciences

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Abstract. The paper is devoted to the problem of robust stability of linear positive discrete-time systems of fractional order with structured perturbations of state matrices. Simple necessary and sufficient conditions for robust stability in the general case and in the case of linear uncertainty structure with unity rank uncertainty structure and with non-negative perturbation matrices, are established. It is shown that robust stability of the positive discrete-time fractional system is equivalent to: 1) robust stability of the corresponding positive discrete-time system of natural order -in the general case, 2) robust stability of the corresponding finite family of positive discrete-time systems of natural order -in the case of linear unity rank uncertainty structure, 3) asymptotic stability of only one corresponding positive discrete-time system of natural order -in the case of linear uncertainty structure with non-negative perturbation matrices. Moreover, simple necessary and sufficient condition for robust stability of the positive interval discrete-time linear systems of fractional order is given. The considerations are illustrated by numerical examples.

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“…It follows from the above considerations and the fact that the positive interval system (36) is robustly stable if and only if the positive system (38) is asymptotically stable [28].…”

Section: Theoremmentioning

confidence: 93%

Robust stability of positive discrete-time linear systems of fractional order

Busłowicz¹

2010

Bulletin of the Polish Academy of Sciences: Technical Sciences

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“…The study of stability of the LTI systems begun approximately one and a half century ago with three important criterions: Hermite in 1856 (Ackermann et al, 1993), 1854 (Bhattacharyya et al, 1995); Routh in 1875 (Ackermann et al, 1993), 1877 (Gantmacher, 1990) and Hurwitz in 1895 (Gantmacher, 1990). Routh, using Sturm's theorem and Cauchy Index theory of a real rational function, set up a theorem to determine the number k of roots of polynomial with real coefficients on the right half plane of the complex numbers.…”

Section: A Recent Stability Criterion For Lti Systemsmentioning

confidence: 99%

“…In industrial reality, there is not a particular system to analyze, there is a family of systems to be analyzed because the values of physical parameters are not known, we know only the lower and upper bounds of each parameter involved in the process, this is known as Parametric Uncertainty (Ackermann et al, 1993;Barmish, 1994;Bhattacharyya et al, 1995). The set of parameters involved in a system makes a Parametric Vector, the set of all vectors that can exists such that each parameter is kept within its lower and upper bounds is called a Parametric Uncertainty Box.…”

Section: Introductionmentioning

confidence: 99%

Parametric Robust Stability

Elizondo-Gonzalez¹

2011

Recent Advances in Robust Control - Theory and Applications in Robotics and Electromechanics

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“…Furthermore, their absence leads to a simpler and interpretable controller structure (see (18) below). Note that in H ∞ optimal controller design quite different criterions (based on a transfer matrix from disturbances to outputs) are used (see Bhattacharyya et al 1995;Sainchez-Pena and Sznaier 1998;Vidyasagar and Kimura 1986;Zhou and Doyle 1998).…”

Section: Fig 1 Extended System and Its Controllermentioning

confidence: 99%

Control of linear extended nD systems with minimized sensitivity to parameter uncertainties

Rafajłowicz

2013

Multidim Syst Sign Process

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A new view on uncertain system parameters is presented considering them in the same way as other independent variables, e.g., time or space variables. After re-interpreting the well known equations for the sensitivities of a system to parameter changes, we consider the problem of optimal control that takes into account not only the quality of control itself, but also a reduction in the influence of parameter changes. Firstly, we re-derive and elucidate known results for systems described by linear ordinary differential equations in the statespace form. Then, it is shown how to extend the well known theory of designing optimal controllers with quadratic criterion so as to cover the reduction of uncertainties in systems described by a class of linear partial differential equations. As a result, we obtain a controller that has a new modal structure in space. Furthermore, the controller incorporates additional sensitivity signals for each mode.

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Robust Control: The Parametric Approach

Cited by 833 publications

References 8 publications

Robust stability of positive discrete-time linear systems of fractional order

Robust stability of positive discrete-time linear systems of fractional order

Parametric Robust Stability

Control of linear extended nD systems with minimized sensitivity to parameter uncertainties

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