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Induced L2Norm Control for LPV Systems with Bounded Parameter Variation Rates
 International Journal of Robust and Nonlinear Control
, 1996
"... A linear, finitedimensional plant, with statespace parameter dependence,... ..."
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Cited by 23 (2 self)
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A linear, finitedimensional plant, with statespace parameter dependence,...
Optimizing dominant time constant in RC circuits
, 1996
"... We propose to use the dominant time constant of a resistorcapacitor (RC) circuit as a measure of the signal propagation delay through the circuit. We show that the dominant time constant is a quasiconvex function of the conductances and capacitances, and use this property to cast several interestin ..."
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Cited by 15 (7 self)
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We propose to use the dominant time constant of a resistorcapacitor (RC) circuit as a measure of the signal propagation delay through the circuit. We show that the dominant time constant is a quasiconvex function of the conductances and capacitances, and use this property to cast several interesting design problems as convex optimization problems, specifically, semidefinite programs (SDPs). For example, assuming that the conductances and capacitances are affine functions of the design parameters (which is a common model in transistor or interconnect wire sizing), one can minimize the power consumption or the area subject to an upper bound on the dominant time constant, or compute the optimal tradeoff surface between power, dominant time constant, and area. We will also note that, to a certain extent, convex optimization can be used to design the topology of the interconnect wires. This approach has two advantages over methods based on Elmore delay optimization. First, it handles a far wider class of circuits, e.g., those with nongrounded capacitors. Second, it always results in convex optimization problems for which very efficient interiorpoint methods have recently been developed. We illustrate the method, and extensions, with several examples involving optimal wire and transistor sizing.
Coordinate Optimization for BiConvex Matrix Inequalities
 In 36 th IEEE Conference on Decision and Control
, 1998
"... We consider optimization of the largest eigenvalue of a smooth selfadjoint matrix valued function \Gamma(X; Y ) of two vector or matrix variables X and Y . We shall assume that \Gamma is concave or convex in Y and separately in X, but possibly has bad joint behavior. A typical problem one faces in ..."
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Cited by 9 (1 self)
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We consider optimization of the largest eigenvalue of a smooth selfadjoint matrix valued function \Gamma(X; Y ) of two vector or matrix variables X and Y . We shall assume that \Gamma is concave or convex in Y and separately in X, but possibly has bad joint behavior. A typical problem one faces in control design are matrix versions of minimizing in Y and maximizing in X. Also minimizing in X and Y is an important problem. When joint behavior in X and Y is bad existing commercial software must be applied to each coordinate separately, and so can be used only to give a coordinate optimization algorithm . We give strong evidence in this article that on "well behaved \Gamma" coordinate optimization always gives a local optimum for the minY maxX problem and that it almost never gives a local solution to the minY minX problem. Also, this article treats second order optimality conditions for optimization of matrix functions. Second order tests are important because optimization of matrix val...
The longstep method of analytic centers for fractional problems
 Mathematical Programming
, 1997
"... We develop a longstep surfacefollowing version of the method of analytic centers for the fractionallinear problem min {t0  t0B(x) − A(x) ∈ H, B(x) ∈ K, x ∈ G}, where H is a closed convex domain, K is a convex cone contained in the recessive cone of H, G is a convex domain and B(·), A(·) are a ..."
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Cited by 6 (1 self)
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We develop a longstep surfacefollowing version of the method of analytic centers for the fractionallinear problem min {t0  t0B(x) − A(x) ∈ H, B(x) ∈ K, x ∈ G}, where H is a closed convex domain, K is a convex cone contained in the recessive cone of H, G is a convex domain and B(·), A(·) are affine mappings. Tracing a twodimensional surface of analytic centers rather than the usual path of centers allows to skip the initial “centering ” phase of the pathfollowing scheme. The proposed longstep policy of tracing the surface fits the best known overall polynomialtime complexity bounds for the method and, at the same time, seems to be more attractive computationally than the shortstep policy, which was previously the only one giving good complexity bounds. 1
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 4 (0 self)
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this article is to provide an overview of the state of the art of