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Control system analysis and synthesis via linear matrix inequalities
 Control Conference, American
, 1982
"... A wide variety of problems in systems and control theory can be cast or recast as convex problems that involve linear matrix inequalities (LMIs). For a few very special cases there are \analytical solutions " to these problems, but in general they can be solved numerically very e ciently. In many ca ..."
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Cited by 13 (1 self)
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A wide variety of problems in systems and control theory can be cast or recast as convex problems that involve linear matrix inequalities (LMIs). For a few very special cases there are \analytical solutions " to these problems, but in general they can be solved numerically very e ciently. In many cases the inequalities have the form of simultaneous Lyapunov or algebraic Riccati inequalities; such problems can be solved in a time that is comparable to the time required to solve the same number of Lyapunov or Algebraic Riccati equations. Therefore the computational cost of extending current control theory that is based on the solution of algebraic Riccati equations to a theory based on the solution of (multiple, simultaneous) Lyapunov or Riccati inequalities is modest. Examples include: multicriterion LQG, synthesis of linear state feedback for multiple or nonlinear plants (\multimodel control"), optimal transfer matrix realization, norm scaling, synthesis of multipliers for Popovlike analysis of systems with unknown gains, and many others. Full details can be found in the references cited. 1.
On Maximizing A Robustness Measure For Structured Nonlinear Perturbations
, 1992
"... In this paper, we propose a robustness measure for LTI systems with causal, nonlinear diagonal perturbations with finite L 2 gain. We propose an algorithm to reliably compute this quantity. We show how to find a statefeedback controller that achieves the global maximum of the robustness measure. 1 ..."
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Cited by 4 (4 self)
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In this paper, we propose a robustness measure for LTI systems with causal, nonlinear diagonal perturbations with finite L 2 gain. We propose an algorithm to reliably compute this quantity. We show how to find a statefeedback controller that achieves the global maximum of the robustness measure. 1. Definition of the Robustness Measure We consider the following feedback system: x = Ax +Bw; z = Cx; (1) w = \Deltaz; (2) where x(t) 2 R n , w(t); z(t) 2 R m , and \Delta is a causal, possibly nonlinear operator mapping L m 2 into itself. We assume that \Delta has `diagonal structure': With z T = [z 1 ; : : : ; z m ] and w T = [w 1 ; : : : ; wm ], we assume that (2) can be expressed as w i = \Delta i (z i ); i = 1; : : : ; m; (3) where each \Delta i maps L 2 into itself. We also assume that (A; B; C) is a minimal realization of the transfer matrix H(s) \Delta = C(sI \Gamma A) \Gamma1 B. Denote by P the set of real diagonal m \Theta m matrices with positive entries and d...
Ghaoui. Numerical methods for H2 related problems
 In Proc. American Control Conf
, 1992
"... Recent results have shown that several H2 and H2related problems can be formulated as convex programs with a nite number of variables. We present an interior point algorithm for the solution of these convex programs and illustrate its application with the standard LQR design. 1. ..."
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Cited by 3 (2 self)
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Recent results have shown that several H2 and H2related problems can be formulated as convex programs with a nite number of variables. We present an interior point algorithm for the solution of these convex programs and illustrate its application with the standard LQR design. 1.