Browsing Biomedical Imaging Lab (Minerva Research Group) by Issue Date
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Degenerations of curves in P³
(Georgia Institute of TechnologyAmerican Mathematical Society, 197801)In this paper we prove every connected, reduced curve in P³ of arithmetic genus 0, may be flatly smoothed. Moreover, we give a new example of a reduced singular curve in P³ which cannot be flatly smoothed. 
A note on linear systems on K3 surfaces
(Georgia Institute of TechnologyAmerican Mathematical Society, 198209)A simple necessary and sufficient condition is given for a general member of the complete linear system Y to be irreducible and nonsingular where Y is a reduced, connected curve on a K3 surface. 
Robust stabilization of systems with uncertain parameters
(Georgia Institute of TechnologyInstitute of Electrical and Electronics Engineers, 198412)This paper considers, from a complex function theoretic point of view, certain robust synthesis problems. We consider both real and complex parameter variations. It is shown that several apparently different problems can ... 
Stabilization of TimeDelay Systems Using FiniteDimensional Compensators
(Georgia Institute of TechnologyInstitute of Electrical and Electronics Engineers, 198501)For linear timeinvariant systems with one or more noncommensurate time delays, necessary and sufficient conditions are given for the existence of a finitedimensional stabilizing feedback compensator. In particular, it ... 
NonEuclidian metrics and the robust stabilization of systems with parameter uncertainty
(Georgia Institute of TechnologyInstitute of Electrical and Electronics Engineers, 198510)This paper considers, from a complex function theoretic point of view, certain kinds of robust synthesis problems. In particular, we use a certain kind of metric on the disk (the "hyperbolic" metric) which allows us to ... 
Robust Control of Linear TimeInvariant Plants Using Periodic Compensation
(Georgia Institute of TechnologyInstitute of Electrical and Electronics Engineers, 198511)This paper considers the use and design of linear periodic timevarying controllers for the feedback control of linear timeinvariant discretetime plants. We will show that for a large class of robustness problems, periodic ... 
Weighted sensitivity minimization of linear periodic timevarying systems
(Georgia Institute of TechnologyInstitute of Electrical and Electronics Engineers, 198512)The problem of weighted sensitivity minimization of linear periodic timevarying plants is considered. The controllers are also required to be linear periodic with the same period as that of the plant. A formula for the ... 
Weighted sensitivity minimization for delay systems
(Georgia Institute of TechnologyInstitute of Electrical and Electronics Engineers, 198512)In this note we discuss the H∞sensitivity minimization problem for linear timeinvariant delay systems. While the unweighted case reduces to simple NevanlinnaPick interpolation, the weighted case turns out to be much ... 
Weighted Sensitivity Minimization for Delay Systems
(Georgia Institute of TechnologyInstitute of Electrical and Electronics Engineers, 198608)In this note we discuss the H ∞ sensitivity minimization problem for linear timeinvariant delay systems. While the unweighted case reduces to simple NevanlinnaPick interpolation, the weighted case turns out to be much ... 
On the sensitivity minimization problem for linear timevarying periodic systems
(Georgia Institute of TechnologySociety for Industrial and Applied Mathematics, 198609)An optimal control problem is formulated in the context of linear, discretetime, periodic systems. The cost is the supremum over all exogenous inputs in a weighted hall of plant inputs. The controller is required to be ... 
H∞Optimization Theory for Distributed Systems
(Georgia Institute of TechnologyInstitute of Electrical and Electronics Engineers, 198612)In this note we write down an explicit formula for the computation of the optimal sensitivity of an arbitrary single input/output, linear timeinvariant distributed plant. We moreover discuss the uniqueness of the optimal ... 
On the H∞ Optimal Sensitivity Problem for Systems with Delays
(Georgia Institute of TechnologySociety for Industrial and Applied Mathematics, 19870501)In this paper we extend some of the results of [IEEE Trans. Automat. Control, AC31 (1986), pp. 763–766] to more general delay systems. In particular, we analyze the effect of the interaction of delays and nonminimum phase ... 
Robotic Manipulators and the Geometry of Real Semialgebraic Sets
(Georgia Institute of TechnologyInstitute of Electrical and Electronics Engineers, 19870801)Some modern techniques are applied from real semialgebraic geometry to the robotic manipulator problem. In particular, using the notion of "metric entropy," the complexity of maneuvering the manipulator from state to state ... 
On the Uniqueness of a Minimal Norm Representative of an Operator in the Commutant of the Compressed Shift
(Georgia Institute of TechnologyAmerican Mathematical Society, 198712)In this note we give a new criterion guaranteeing the uniqueness of a minimal norm representative of a bounded linear operator which commutes with a finite multiplicity shift. We moreover give examples which show that ... 
Spectral NevanlinnaPick interpolation theory and robust stabilization
(Georgia Institute of TechnologyInstitute of Electrical and Electronics Engineers, 198712)In this note we will discuss a new kind of interpolation theory in which one bounds the spectral radius of the matrixvalued interpolating functions instead of the norm as is the case with ordinary NevanlinnaPick ... 
On the spectra and invertibility of certain operators in systems theory
(Georgia Institute of TechnologyInstitute of Electrical and Electronics Engineers, 198712)In this paper we study the following kind of problem. Let T be an arbitrary contraction. We will define a certain function which will lead to an explicit procedure for the computation of the isolated spectrum of w(T)w(T)', ... 
Some explicit formulae for the singular values of certain hankel operators with factorizable symbol
(Georgia Institute of TechnologySociety for Industrial and Applied Mathematics, 198809)In this paper a determinantal formula is written that allows one to compute the singular values of Hankel operators, the L∞ symbols of which are of the form mw for WE H∞ rational and mE H∞ inner. (All of the Hardy spaces ... 
The four block problem for distributed systems
(Georgia Institute of TechnologyInstitute of Electrical and Electronics Engineers, 198812)A study is made of the singular values of the fourblock operator, which appears naturally in many H∞ control problems. Following the framework of the monograph of B.A. Francis (1987), almost all such robust design problems ... 
Remarks on H∞ optimization multivariate distributed systems
(Georgia Institute of TechnologyInstitute of Electrical and Electronics Engineers, 198812)The results of a study of H∞optimization for multivariable distributed systems are summarized. A skew Toeplitz framework has been used. The problem has been reduced to finding the singular values of a certain operator ... 
A strong Parrot theorem
(Georgia Institute of TechnologyAmerican Mathematical Society, 198907)In this note we discuss a strengthened version of a theorem due to Parrott [8] in operator dilation theory. We relate our result to the onestep extension procedure of AdamjanArovKrein [1].