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141
Randomized Algorithms for Analysis and Control of Uncertain Systems
 in Perspectives in Robust Control
, 2001
"... Undoubtedly, model uncertainty and robustness have been key themes in the development of modern automatic control during the last four decades. In fact, in many situations feedback control of dynamical systems allows to substantially improve typical control engineering objectives, such as accurate p ..."
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Cited by 83 (23 self)
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Undoubtedly, model uncertainty and robustness have been key themes in the development of modern automatic control during the last four decades. In fact, in many situations feedback control of dynamical systems allows to substantially improve typical control engineering objectives, such as accurate pathfollowing or effective disturbance attenuation, even if only a rather poor mathematical model of the tobecontrolled dynamics is available. On the other hand, optimizationbasedcontroller design strategies typically rely on a sufficiently accurate model of the tobecontrolled plant. Recent years have witnessedthe development of techniques for quantifying the plantmodel mismatch, such as in uncertainty estimation basedon measureddata or as resulting from model reduction to reduce complexity. Various widely used paradigms for the mathematical description
Robust Pole Placement in LMI Regions
 IEEE Transactions on Automatic Control
, 1999
"... This paper discusses analysis and synthesis techniques for robust pole placement in LMI regions, a class of convex regions of the complex plane that embraces most practically useful stability regions. The focus is on linear systems with static uncertainty on the state matrix. For this class of uncer ..."
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Cited by 46 (0 self)
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This paper discusses analysis and synthesis techniques for robust pole placement in LMI regions, a class of convex regions of the complex plane that embraces most practically useful stability regions. The focus is on linear systems with static uncertainty on the state matrix. For this class of uncertain systems, the notion of quadratic stability and the related robustness analysis tests are generalized to arbitrary LMI regions. The resulting tests for robust pole clustering are all numerically tractable since they involve solving linear matrix inequalities (LMIs), and cover both unstructured and parameter uncertainty. These analysis results are then applied to the synthesis of dynamic outputfeedback controllers that robustly assign the closedloop poles in a prescribed LMI region. With some conservatism, this problem is again tractable via LMI optimization. In addition, robust pole placement can be combined with other control objectives such as H 2 or H1 performance to capture realist...
Robustness Analysis of Polynomials with Polynomial Parameter Dependency Using Bernstein Expansion
 IEEE TRANS. AUTOMAT. CONTR
, 1998
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Global Optimization in Generalized Geometric Programming
 Engng
, 1997
"... A deterministic global optimization algorithm is proposed for locating the global minimum of generalized geometric (signomial) problems (GGP). By utilizing an exponential variable transformation the initial nonconvex problem (GGP) is reduced to a (DC) programming problem where both the constraints ..."
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Cited by 17 (3 self)
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A deterministic global optimization algorithm is proposed for locating the global minimum of generalized geometric (signomial) problems (GGP). By utilizing an exponential variable transformation the initial nonconvex problem (GGP) is reduced to a (DC) programming problem where both the constraints and the objective are decomposed into the difference of two convex functions. A convex relaxation of problem (DC) is then obtained based on the linear lower bounding of the concave parts of the objective function and constraints inside some box region. The proposed branch and bound type algorithm attains finite fflconvergence to the global minimum through the successive refinement of a convex relaxation of the feasible region and/or of the objective function and the subsequent solution of a series of nonlinear convex optimization problems. The efficiency of the proposed approach is enhanced by eliminating variables through monotonicity analysis, by maintaining tightly bound variables thro...
Worstcase properties of the uniform distribution and randomized algorithms for robustness analysis
 Mathematics of Control, Signals, and Systems
, 1998
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Robust control of polytopic systems by convex optimization. Automatica
, 2007
"... Abstract—Robust control synthesis of linear timeinvariant SISO polytopic systems is investigated using the polynomial approach. A convex set of all stabilizing controllers for a polytopic system is given over an infinitedimensional space. A finitedimensional approximation of this set is obtained ..."
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Cited by 16 (1 self)
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Abstract—Robust control synthesis of linear timeinvariant SISO polytopic systems is investigated using the polynomial approach. A convex set of all stabilizing controllers for a polytopic system is given over an infinitedimensional space. A finitedimensional approximation of this set is obtained using the orthonormal basis functions and represented by a set of LMIs thanks to the KYP lemma. Then, an LMI based convex optimization problem for robust pole placement with sensitivity function shaping in two and infinitynorm is proposed. The simulation results show the effectiveness of the proposed method. I.
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 13 (10 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...
Criteria for robust absolute stability of timevarying nonlinear continuoustime systems
 AUTOMATICA
, 2002
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Distributionally robust monte carlo simulation: A tutorial survey
 Proceedings of the IFAC World Congress. Barcelona,Spain
, 2002
"... Whereas the use of traditional Monte Carlo simulation requires probability distributions for the uncertain parameters entering the system, distributionally robust Monte Carlo simulation does not. The description of this new approach to Monte Carlo simulation is the focal point of this tutorial sur ..."
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Cited by 9 (0 self)
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Whereas the use of traditional Monte Carlo simulation requires probability distributions for the uncertain parameters entering the system, distributionally robust Monte Carlo simulation does not. The description of this new approach to Monte Carlo simulation is the focal point of this tutorial survey. According to the new theory, instead of carrying out simulations using some rather arbitrary probability distribution such as Gaussian for the uncertain parameters, we provide a rather different prescription based on distributional robustness considerations. The new approach which we describe, does not require a probability distribution f for the uncertain parameters. Instead, motivated by manufacturing considerations, a class of distributions F is specified and the results of the simulation hold for all f ∈ F. In a sense, this new method of Monte Carlo simulation was developed with the robustician in mind. That is, the motivation for this new approach is derived from the fact that robusticians often object to classical Monte Carlo simulation on the grounds that the probability distribution for the uncertain parameters is unavailable. They typically begin only with bounds on the uncertain parameters and are unwilling to assume an a priori probability distribution. This is the same starting point for the methods provided here.
Parameterdependent Lyapunov functions for stability analysis of LTI parameter dependent systems
 in Proceedings of the IEEE 42nd Conference on Decision and Control, 2003
, 2003
"... Abstract — In this paper, we propose a class of parameterdependent Lyapunov functions which can be used to assess the stability properties of linear, timeinvariant, singleparameter dependent (LTIPD) systems in a nonconservative manner. It is shown that stability of LTIPD systems is equivalent to ..."
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Cited by 9 (3 self)
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Abstract — In this paper, we propose a class of parameterdependent Lyapunov functions which can be used to assess the stability properties of linear, timeinvariant, singleparameter dependent (LTIPD) systems in a nonconservative manner. It is shown that stability of LTIPD systems is equivalent to the existence of a Lyapunov function of a polynomial type (in terms of the parameter) of known, bounded degree satisfying two matrix inequalities. It is also shown that checking the feasibility of these matrix inequalities over a compact set can be cast as a convex optimization problem. I.