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Wallace H. Coulter Department of Biomedical Engineering
Wallace H. Coulter Department of Biomedical Engineering
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ItemCausal power series and the nonlinear standard H∞ problem(Georgia Institute of Technology, 199712) Foias, Ciprian ; Gu, Caixing ; Tannenbaum, Allen R.Using a power series approach, we describe a design procedure applicable to analytic nonlinear plants. Our technique is a generalization of the linear H∞ theory. We can now use this theory to solve the full standard problem in robust control theory in the nonlinear framework

ItemThe structured singular value for linear input/output systems(Georgia Institute of Technology, 199607) Bercovici, Hari ; Foias, Ciprian ; Tannenbaum, Allen R.In this paper, we employ our lifting method to study the structured singular value applied to input/output operators of control systems. We moreover give a new criterion which guarantees that the structured singular value equals its upper bound defined by $D$scalings.

ItemNonlinear H∞ Optimization: A Causal Power Series Approach(Georgia Institute of Technology, 199501) Foias, Ciprian ; Gu, Caixing ; Tannenbaum, Allen R.In this paper, using a power series methodology a design procedure applicable to analytic nonlinear plants is described. The technique used is a generalization of the linear H∞ theory. In contrast to previous work on this topic ([Indiana J. Math., 36 (1987), pp. 693–709], [Oper. Theory Adv. Appl., 41 (1989), pp. 255–277], [SIAM J. Control Optim., 27 (1989), pp. 842–860] ), the authors are now able to incorporate explicitly a causality constraint into the theory. In fact, it is shown that it is possible to reduce a causal optimal design problem (for nonlinear systems) to a classical interpolation problem solvable by the commutant lifting theorem [Harmonic Analysis of Operators on Hilbert Space, NorthHolland, Amsterdam, 1970], [The Commutant Lifitng Approach to Interpolation Problems, Birkhäuser, Boston, 1990].

ItemOn structured tangential NevanlinnaPick interpolation(Georgia Institute of Technology, 199312) Bercovici, Hari ; Cockburn, Juan C. ; Foias, Ciprian ; Tannenbaum, Allen R.This paper is a continuation of the work of BercoviciFoiasTannenbaum (1989,1990) on interpolation problems where the interpolating functions are bounded not in norm but in spectral radius or structured singular values. These problems arise naturally in the robust control of systems with structured uncertainty. Here we extend our structured matrix NevanlinnaPick interpolation theory to the (onesided) tangential case. With these results, we have laid the groundwork for a rigorous analytic procedure for μsynthesis.

ItemA Spectral Commutant Lifting Theorem(Georgia Institute of Technology, 199106) Bercovici, Hari ; Foias, Ciprian ; Tannenbaum, Allen R.

ItemStructured interpolation and robust control(Georgia Institute of Technology, 199012) Bercovici, Hari ; Foias, Ciprian ; Tannenbaum, Allen R.The authors extend their previous work on the spectral commutant lifting theorem to the case of structured singular values which appear in certain problems in control theory. They also give a new characterization of the structured singular value and formulate and prove a structured version of the matrix NevanlinnaPick theorem.

ItemSpectral Tangential Interpolation and Gain Margin Problems(Georgia Institute of Technology, 199005) Bercovici, Hari ; Foias, Ciprian ; Tannenbaum, Allen R.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 interpolation. We relate this to the multivariable gain margin problem.

ItemSpectral radius interpolation and robust control(Georgia Institute of Technology, 198912) 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.

ItemOn the Nonlinear Mixed Sensitivity Problem(Georgia Institute of Technology, 198912) Foias, Ciprian ; Tannenbaum, Allen R. ; Enns, Dale ; Georgiou, Tryphon T. ; Jackson, Michael ; Schipper, BrianThe nonlinear H∞ synthesis theory for the sensitivity minimization problem is extended to the twoblock 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 nlinear 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.

ItemA strong Parrot theorem(Georgia Institute of Technology, 198907) 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 onestep extension procedure of AdamjanArovKrein [1].