Organizational Unit:
Wallace H. Coulter Department of Biomedical Engineering

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https://ror.org/02j15s898
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Publication Search Results

Now showing 1 - 10 of 26
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    Spectral radius interpolation and robust control
    (Georgia Institute of Technology, 1989-12) Bercovici, Hari ; Foias, Ciprian ; Tannenbaum, Allen R.
    In a previous paper (1987) Tannenbaum discussed an interpolation problem closely related to the multivariate gain margins of J.C. Doyle (1984) and M.G. Safonov (1980). For this interpolation problem, it is necessary to interpolate on the disk with analytic matrices of bounded spectral radius instead of norm.
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    Robust control design for a flexible beam using a distributed-parameter H∞-method
    (Georgia Institute of Technology, 1989-12) Lenz, Kathryn ; Özbay, Hitay ; Tannenbaum, Allen R. ; Turi, Janos ; Morton, Blaise
    A skew Toeplitz theory is used to derive the H∞-optimal controller for a weighted mixed sensitivity design for a free-free Euler-Bernoulli beam. On the basis of the structure of the optimal controller, low-order, suboptimal, finite-dimensional, linear, time-invariant controllers are designed for the beam with and without a pure time delay.
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    Control of Slowly-Varying Linear Systems
    (Georgia Institute of Technology, 1989-12) Kamen, Edward W. ; Khargonekar, Pramod P. ; Tannenbaum, Allen R.
    State feedback control of slowly varying linear continuous-time and discrete-time systems with bounded coefficient matrices is studied in terms of the frozen-time approach. This study centers on pointwise stabilizable systems. These are systems for which there exists a state feedback gain matrix placing the frozen-time closed-loop eigenvalues to the left of a line Re s=-γ<0 in the complex plane (or within a disk of radius ρ<1 in the discrete-time case). It is shown that if the entries of a pointwise stabilizing feedback gain matrix ar continuously differentiable functions of the entries of the system coefficient matrices, then the closed-loop system is uniformly asymptotically stable if the rate of time variation of the system coefficient matrices is sufficiently small. It is also shown that for pointwise stabilizable systems with a sufficiently slow rate of time variation in the system coefficients, a stabilizing feedback gain matrix can be computed from the positive definite solution of a frozen-time algebraic Riccati equation.
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    On approximately optimal H∞ controllers for distributed systems
    (Georgia Institute of Technology, 1989-12) Özbay, Hitay ; Tannenbaum, Allen R.
    The structure of all approximately optimal H∞ controllers for stable distributed plants with rational weights is elucidated. The finite- and infinite-dimensional parts of these H ∞ controllers are identified. It is shown that one can obtain a finite-dimensional approximately optimal controller by appropriately approximating the infinite-dimensional part of the optimal controller. Also, it is possible to find certain bounds on the deviation from optimal performance using this procedure.
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    A solution to the standard H∞ problem for multivariable distributed systems
    (Georgia Institute of Technology, 1989-12) Özbay, Hitay ; Tannenbaum, Allen R.
    The authors summarize the results of previous work in which they studied the problem of the H∞ optimal control of multivariable distributed systems in the four-block setting. The skew Toeplitz framework is employed.
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    On the Nonlinear Mixed Sensitivity Problem
    (Georgia Institute of Technology, 1989-12) Foias, Ciprian ; Tannenbaum, Allen R. ; Enns, Dale ; Georgiou, Tryphon T. ; Jackson, Michael ; Schipper, Brian
    The nonlinear H∞ synthesis theory for the sensitivity minimization problem is extended to the two-block mixed sensitivity method. The synthesis method is valid for majorizable input/output operators and can be extended to operators that can be approximated by them. In particular, operators that are analytic in a ball around the origin in a complex Hilbert space are considered. It turns out that it is possible to express each n-linear term of the Taylor expansion of such an operator on a certain tensor space. In the development of the theory, some of the Toeplitz techniques are extended to linear operators defined on certain tensor spaces.
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    A strong Parrot theorem
    (Georgia Institute of Technology, 1989-07) Foias, Ciprian ; Tannenbaum, Allen R.
    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 one-step extension procedure of Adamjan-Arov-Krein [1].
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    Weighted Optimization Theory for Nonlinear Systems
    (Georgia Institute of Technology, 1989-07) Foias, Ciprian ; Tannenbaum, Allen R.
    In this paper, the solution of a nonlinear version of the weighted sensitivity H∞-optimization problem is discussed. It is shown that the natural object to be considered in this context is a certain "sensitivity operator," which will be optimized locally in a given "energy ball" (see §5 for the details). In the linear case, the authors are reduced again to the classical sensitivity minimization technique of Zames [21]. The methods were very strongly influenced by the complex analytic power series ideas of [3], [4], [5]. See also the recent results of Ball and Helton [6] for another approach to this subject.
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    Remarks on H∞ optimization multivariate distributed systems
    (Georgia Institute of Technology, 1988-12) Foias, Ciprian ; Özbay, Hitay ; Tannenbaum, Allen R.
    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 (the so-called four-block operator). Depending on the specific problem considered, the corresponding four-block operator can be simplified to a two-block or one-block operator. This is specialized to the multivariate two-block case. A procedure for the computation of the eigenvalues of this operator is described.
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    The four block problem for distributed systems
    (Georgia Institute of Technology, 1988-12) Foias, Ciprian ; Tannenbaum, Allen R.
    A study is made of the singular values of the four-block 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 can be formulated in terms of the spectral properties of such an operator. This includes the problems of sensitivity and mixed-sensitivity minimization, model matching, and certain tracking problems. The authors' techniques give the optimal solution to this problem, which is valid for a large class of distributed systems.