Showing papers on "Dual norm published in 1995"
TL;DR: A new approach can be used to characterize the completions that minimize the norm of the inverse and the condition number with respect to the spectral norm when a submatrix of a matrix can be chosen arbitrarily.
Abstract: We study the problem of minimizing the norm, the norm of the inverse and the condition number with respect to the spectral norm, when a submatrix of a matrix can be chosen arbitrarily. For the norm minimization problem we give a different proof than that given by Davis/Kahan/Weinberger. This new approach can then also be used to characterize the completions that minimize the norm of the inverse. For the problem of optimizing the condition number we give a partial result.
15 citations
TL;DR: It is shown in this paper that, given precise or certain partial knowledge of the poles of the transfer function, it is possible to obtain an upper bound of the H-infinity norm as a function of theH-2 norm, both in the continuous and discrete time cases.
15 citations
21 Jun 1995
TL;DR: In this paper, the authors show using examples that minimizing the star norm does not necessarily imply good peak-to-peak disturbance rejection, and they show that the *-norm does not always imply good P2P rejection.
Abstract: This paper pertains to the results obtained in Nagpal et al. (1994) where the authors present a norm, which they call the "*-norm", and conclude that minimizing the star norm results in good peak to peak disturbance rejection. The problem they treat reduces to solving a set of parameter dependent LMIs for standard synthesis problems in control and estimation. In this paper, the authors show using examples that minimizing the star norm does not necessarily imply good peak to peak disturbance rejection.
14 citations
TL;DR: This paper answers the question of whether (or not) there exist normed input-output vector spaces that induce the Frobenius matrix norm by using the notion of dual norms and shows that the maximum singular value is the only unitarily invariant induced norm.
Abstract: In this paper we answer the question of whether (or not) there exist normed input-output vector spaces that induce the Frobenius matrix norm. Specifically, using the notion of dual norms we show that, up to a scalar multiple, the maximum singular value is the only unitarily invariant induced norm. As a special case of this result, it follows that the Frobenius matrix norm is not induced.
13 citations
TL;DR: The authors show that the Hankel norm is equal to that of an equivalent discrete-time system and demonstrate two simple examples including sampled-data controller reduction.
Abstract: Generalizes the concept of Hankel norm for purely continuous-time systems to sampled-data systems. The Hankel norm of a sampled-data system is defined by taking into account intersample behaviors. The formula of the Hankel norm of a sampled-data system is given by a hybrid state-space model approach. The authors show that the Hankel norm is equal to that of an equivalent discrete-time system. Two simple examples including sampled-data controller reduction are demonstrated. >
8 citations
TL;DR: In this article, a strictly convex, reflexive, smooth Banach space has a Chebyshev subspace M such that the projection onto M is linear and has norm equal to 2.
2 citations