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Algorithms and Software for LMI Problems in Control
 IEEE Control Systems Magazine
, 1997
"... this article is to provide an overview of the state of the art of ..."
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Cited by 8 (0 self)
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this article is to provide an overview of the state of the art of
Global Optimization with Polynomials and the Problem of Moments
 SIAM JOURNAL ON OPTIMIZATION
, 2001
"... We consider the problem of finding the unconstrained global minimum of a realvalued polynomial p(x) : R R, as well as the global minimum of p(x), in a compact set K defined by polynomial inequalities. It is shown that this problem reduces to solving an (often finite) sequence of convex linear ma ..."
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Cited by 577 (48 self)
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matrix inequality (LMI) problems. A notion of KarushKuhnTucker polynomials is introduced in a global optimality condition. Some illustrative examples are provided.
A Sequential SDP/GaussNewton Algorithm for RankConstrained LMI Problems
 Proceedings of the 38 th Conference on Decision and Control
, 1999
"... This paper develops a secondorder Newton algorithm for finding local solutions of rankconstrained LMI problems in robust synthesis. The algorithm is based on a quadratic approximation of a suitably defined merit function and generates sequences of LMI feasible iterates. The main trust of the algor ..."
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Cited by 3 (0 self)
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This paper develops a secondorder Newton algorithm for finding local solutions of rankconstrained LMI problems in robust synthesis. The algorithm is based on a quadratic approximation of a suitably defined merit function and generates sequences of LMI feasible iterates. The main trust
Loworder Control Design for LMI Problems Using Alternating Projection Methods*
"... Computational techniques that exploit the geometry of the design space are proposed to solve fixedorder control design problems described in terms of linear matrix inequalities and a coupling rank constraint. Key WordsControl systems design; loworder controllers; statespace methods; H" con ..."
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Computational techniques that exploit the geometry of the design space are proposed to solve fixedorder control design problems described in terms of linear matrix inequalities and a coupling rank constraint. Key WordsControl systems design; loworder controllers; statespace methods; H
Asymptotically exact relaxations for robust LMI problems based on matrixvalued sumofsquares
 In Proceedings of the International Symposium on Mathematical Theory of Networks and Systems (MTNS
, 2004
"... In this paper we consider the problem of characterizing whether a symmetric polynomial matrix is positive definite on a semialgebraic set. Based on suitable sumofsquares representations we can construct LMI relaxation for this decision problem. As key novel technical contributions it is possible ..."
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Cited by 4 (0 self)
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In this paper we consider the problem of characterizing whether a symmetric polynomial matrix is positive definite on a semialgebraic set. Based on suitable sumofsquares representations we can construct LMI relaxation for this decision problem. As key novel technical contributions it is possible
Multiobjective output feedback control via LMI
 in Proc. Amer. Contr. Conf
, 1997
"... The problem of multiobjective H2=H1 optimal controller design is reviewed. There is as yet no exact solution to this problem. We present a method based on that proposed by Scherer [14]. The problem is formulated as a convex semidefinite program (SDP) using the LMI formulation of the H2 and H1 norms. ..."
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Cited by 220 (8 self)
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The problem of multiobjective H2=H1 optimal controller design is reviewed. There is as yet no exact solution to this problem. We present a method based on that proposed by Scherer [14]. The problem is formulated as a convex semidefinite program (SDP) using the LMI formulation of the H2 and H1 norms
LMI Approach
"... Abstract: By using the Lyapunov second method, the robust control and robust optimal control for the gas tungsten arc welding dynamic process whose underlying continuoustime systems are subjected to structured uncertainties are discussed in timedomain. As results, some sufficient conditions of ro ..."
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of robust stability and the corresponding robust control laws are derived. All these results are designed by solving a class of linear matrix inequalities (LMIs) and a class of dynamic optimization problem with LMIs constraints respectively. An example adapted under some experimental conditions
LMITOOL: a Package for LMI Optimization
 In Proceedings of the IEEE Conference on Decision and Control
, 1995
"... Many problems in systems and control can be formulated as "Linear Matrix Inequality" (LMI) problems. Recently, efficient algorithms have been developed for solving LMI's of reasonable size. Using these programs for solving control problems however requires a reformulation of the probl ..."
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Cited by 17 (1 self)
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Many problems in systems and control can be formulated as "Linear Matrix Inequality" (LMI) problems. Recently, efficient algorithms have been developed for solving LMI's of reasonable size. Using these programs for solving control problems however requires a reformulation
A Rank Minimization Heuristic with Application to Minimum Order System Approximation
, 2001
"... Several problems arising in control system analysis and design, such as reduced order controller synthesis, involve minimizing the rank of a matrix variable subject to linear matrix inequality (LMI) constraints. Except in some special cases, solving this rank minimization probiem (globally) is ve ..."
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Cited by 274 (10 self)
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Several problems arising in control system analysis and design, such as reduced order controller synthesis, involve minimizing the rank of a matrix variable subject to linear matrix inequality (LMI) constraints. Except in some special cases, solving this rank minimization probiem (globally
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 47 (0 self)
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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
Results 1  10
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