Christopher I. Byrnes

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In this paper, we derive conditions under which a nonlinear system can be rendered passive via smooth state feedback and we show that, as in the case linear systems, this is possible if and only if the system in question has relative degree 1 and is weakly minimum phase. Then, we prove that weakly minimum phase nonlinear systems having relative degree 1 can(More)
In a seminal paper, Sarason generalized some classical interpolation problems for H∞ functions on the unit disc to problems concerning lifting onto H2 of an operator T that is defined on K= H2 φH2 (φ is an inner function) and commutes with the (compressed) shift S. In particular, he showed that interpolants (i.e., f ∈ H∞ such that f(S) = T ) having norm(More)
In this paper, we present a generalized entropy criterion for solving the rational Nevanlinna–Pick problem for + 1 interpolating conditions and the degree of interpolants bounded by . The primal problem of maximizing this entropy gain has a very well-behaved dual problem. This dual is a convex optimization problem in a finite-dimensional space and gives(More)
In this paper we present a convex optimization problem for solving the rational covariance extension problem. Given a partial covariance sequence and the desired zeros of the modeling filter, the poles are uniquely determined from the unique minimum of the corresponding optimization problem. In this way we obtain an algorithm for solving the covariance(More)
This work extends the geometric theory of output regulation to linear distributed parameter systems with bounded input and output operator, in the case when the reference signal and disturbances are generated by a finite dimensional exogenous system. In particular, it is shown that the full state feedback and error feedback regulator problems are solvable,(More)
Traditional maximum entropy spectral estimation determines a power spectrum from covariance estimates. Here, we present a new approach to spectral estimation, which is based on the use of filter banks as a means of obtaining spectral interpolation data. Such data replaces standard covariance estimates. A computational procedure for obtaining suitable(More)
The trigonometric moment problem is a classical moment problem with numerous applications in mathematics, physics, and engineering. The rational covariance extension problem is a constrained version of this problem, with the constraints arising from the physical realizability of the corresponding solutions. Although the maximum entropy method gives one(More)