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77
Applications Of Quantifier Elimination Theory To Control System Design
 IN 4TH IEEE MEDITERRANEAN SYMPOSIUM ON CONTROL AND AUTOMATION
, 1996
"... In this paper we show how a number of interesting linear control system analysis and design problems can be reduced to Quantifier Elimination (QE) problems. We assume a fixed structure for the compensator, with design parameters q i . The problems considered are problems that currently have no gene ..."
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Cited by 21 (4 self)
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In this paper we show how a number of interesting linear control system analysis and design problems can be reduced to Quantifier Elimination (QE) problems. We assume a fixed structure for the compensator, with design parameters q i . The problems considered are problems that currently have no general solution. However, the problems must be of modest complexity if existing QE software packages are to produce answers. The software package QEPCAD is used to solve some numerical design examples.
Positive Polynomials and Robust Stabilization with FixedOrder Controllers
 IEEE Transactions on Automatic Control
, 2002
"... Recent results on positive polynomials are used to obtain a convex inner approximation of the stability domain in the space of coe#cients of a polynomial. An application to the design of fixedorder controllers robustly stabilizing a linear system subject to polytopic uncertainty is then proposed ..."
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Cited by 20 (13 self)
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Recent results on positive polynomials are used to obtain a convex inner approximation of the stability domain in the space of coe#cients of a polynomial. An application to the design of fixedorder controllers robustly stabilizing a linear system subject to polytopic uncertainty is then proposed, based on LMI optimization.
An LMI Condition for Robust Stability of Polynomial Matrix Polytopes
, 2000
"... A sufficient LMI condition is proposed for checking robust stability of a polytope of polynomial matrices. It hinges upon two recent results: a new approach to polynomial matrix stability analysis and a new robust stability condition for convex polytopic uncertainty. Numerical experiments illustrate ..."
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Cited by 12 (9 self)
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A sufficient LMI condition is proposed for checking robust stability of a polytope of polynomial matrices. It hinges upon two recent results: a new approach to polynomial matrix stability analysis and a new robust stability condition for convex polytopic uncertainty. Numerical experiments illustrate that the condition narrows significantly the unavoidable gap between conservative tractable quadratic stability results and exact NPhard robust stability results. Keywords Polynomial matrix, Parametric uncertainty, Robust stability, Quadratic stability, LMI. This work has been supported by the Barrande Project No. 97/00597/026, by the Grant Agency of the Czech Republic under contract No. 102/99/1368 and by the Ministry of Education of the Czech Republic under contract No. VS97/034. y Corresponding author. Email henrion@laas.fr. FAX 33 5 61 33 69 69. Introduction Polynomial matrices appear as a key tool for studying systems control. Dynamics of many systems (e.g. lightly damped st...
Ellipsoidal Approximation of the Stability Domain of a Polynomial
 Proceedings of the European Control Conference
, 2000
"... The stability region in the space of coefficients of a polynomial is a nonconvex region in general. In this paper, we propose a new convex ellipsoidal inner approximation of this region derived via optimization over linear matrix inequalities. As a byproduct, we obtain new simple sufficient cond ..."
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Cited by 8 (7 self)
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The stability region in the space of coefficients of a polynomial is a nonconvex region in general. In this paper, we propose a new convex ellipsoidal inner approximation of this region derived via optimization over linear matrix inequalities. As a byproduct, we obtain new simple sufficient conditions for stability that may prove useful in robust control design. Keywords Polynomial, Stability, LMI. 1 Introduction Consider an nth degree monic polynomial x(s) = x 0 + x 1 s + \Delta \Delta \Delta + x n\Gamma1 s n\Gamma1 + s n : The problem of finding simple conditions in the ndimensional Euclidean space of real coefficients x 0 ; x 1 ; : : : ; x n\Gamma1 under which the roots of x(s) are located in a given region 1 Corresponding author. FAX: +33 5 61 33 69 69. Email: henrion@laas.fr 2 Laboratoire d'Analyse et d'Architecture des Syst`emes, Centre National de la Recherche Scientifique, 7 Avenue du Colonel Roche, 31 077 Toulouse, cedex 4, France. 3 Center for Applied Cy...
Fault diagnosis and fault tolerant control using set–membership approaches: application to real case studies
 Int. J. Appl. Math. Comput. Sci
"... This paper reviews the use of setmembership methods in fault diagnosis (FD) and fault tolerant control (FTC). Setmembership methods use a deterministic unknownbutbounded description of noise and parametric uncertainty (interval models). These methods aims at checking the consistency between obser ..."
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Cited by 4 (0 self)
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This paper reviews the use of setmembership methods in fault diagnosis (FD) and fault tolerant control (FTC). Setmembership methods use a deterministic unknownbutbounded description of noise and parametric uncertainty (interval models). These methods aims at checking the consistency between observed and predicted behaviour by using simple sets to approximate the exact set of possible behaviour (in the parameter or the state space). When an inconsistency is detected between the measured and predicted behaviours obtained using a faultless system model, a fault can be indicated. Otherwise, nothing can be stated. The same principle can be used to identify interval models for fault detection and to develop methods for fault tolerance evaluation. Finally, some real applications will be used to illustrate the usefulness and performance of setmembership methods for FD and FTC.
Robust stability of positive continuoustime linear systems with delays
 International Journal of Applied Mathematics and Computer Science 20(4): 665– 670, DOI
, 2010
"... The paper is devoted to the problem of robust stability of positive continuoustime linear systems with delays with structured perturbations of state matrices. Simple necessary and sufficient conditions for robust stability in the general case and in the case of systems with a linear uncertainty str ..."
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Cited by 4 (1 self)
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The paper is devoted to the problem of robust stability of positive continuoustime linear systems with delays with structured perturbations of state matrices. Simple necessary and sufficient conditions for robust stability in the general case and in the case of systems with a linear uncertainty structure in two subcases: (i) a unity rank uncertainty structure and (ii) nonnegative perturbation matrices are established. The problems are illustrated with numerical examples.
On inverse halftoning: computational complexity and interval computations
 John Hopkins University
, 2005
"... Abstract — We analyze the problem of inverse halftoning. This problem is a particular case of a class of difficulttosolve problems: inverse problems for reconstructing piecewise smooth images. We show that this general problem is NPhard. We also propose a new idea for solving problems of this ty ..."
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Cited by 4 (2 self)
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Abstract — We analyze the problem of inverse halftoning. This problem is a particular case of a class of difficulttosolve problems: inverse problems for reconstructing piecewise smooth images. We show that this general problem is NPhard. We also propose a new idea for solving problems of this type, including the inverse halftoning problem. Need for halftoning I.
Robust SPR synthesis for loworder polynomial segments and interval polynomials
 Proceedings of the American Control Conference (ACC 2001), Crystal Gateway Marriott
, 2001
"... Abstract: We prove that, for loworder (n ≤ 4) stable polynomial segments or interval polynomials, there always exists a fixed polynomial such that their ratio is SPRinvariant, thereby providing a rigorous proof of Anderson’s claim on SPR synthesis for the fourthorder stable interval polynomials. ..."
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Cited by 3 (1 self)
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Abstract: We prove that, for loworder (n ≤ 4) stable polynomial segments or interval polynomials, there always exists a fixed polynomial such that their ratio is SPRinvariant, thereby providing a rigorous proof of Anderson’s claim on SPR synthesis for the fourthorder stable interval polynomials. Moreover, the relationship between SPR synthesis for loworder polynomial segments and SPR synthesis for loworder interval polynomials is also discussed.
Loworder Robust Controller Synthesis for Interval Plants
 International Journal of Control
, 1998
"... This paper deals with robust controller synthesis for SISO linear plants subject to interval parametric uncertainty, a longstanding open problem of control theory. Based on HermiteFujiwara matrices and the Generalized Kharitonov's Theorem, a necessary and sufficient condition is derived for th ..."
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Cited by 3 (2 self)
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This paper deals with robust controller synthesis for SISO linear plants subject to interval parametric uncertainty, a longstanding open problem of control theory. Based on HermiteFujiwara matrices and the Generalized Kharitonov's Theorem, a necessary and sufficient condition is derived for the existence of a robustly stabilizing controller of given order. This condition is formulated as a nonconvex rankone LMI feasibility problem in the controller parameters. Two heuristics are then proposed to handle this key optimization problem, namely a potential reduction algorithm and a Frank and Wolfe gradient algorithm. Both algorithms hinge upon standard semidefinite programming techniques. Several numerical examples bear out the usefulness of our approach for designing robust controllers of small order at low computational cost. 1 Introduction We focus on the problem of robust stabilization of an uncertain singleinput singleoutput plant whose parameters belong to given real intervals. ...
On the Conditioning of Robustness Problems
, 2003
"... This focal point of this paper is the "conditioning" of robustness problems with performance specifications depending nonlinearly on uncertain parameters. Beginning with a rather general class of such problems, we define our socalled underlying conditioner #. For large classes ..."
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Cited by 2 (1 self)
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This focal point of this paper is the "conditioning" of robustness problems with performance specifications depending nonlinearly on uncertain parameters. Beginning with a rather general class of such problems, we define our socalled underlying conditioner #. For large classes