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The Schatten p-norm condition of the discrete-time Lyapunov operator L A defined on matrices P 2 R nn by L A P P ? APA T is studied for stable matrices A 2 R nn. Bounds are obtained for the norm of L A and its inverse that depend on the spectrum, singular values and radius of stability of A. Since the solution P of the the discrete-time algebraic Lyapunov(More)
The purpose of this paper is to classify the solutions of Riemann problems near a hyperbolic singularity in a nonlinear system of conservation laws. Hyperbolic singularities play the role in the theory of Riemann problems that rest points play in the theory of ordinary differential equations: Indeed, generically, only a finite number of structures can(More)
Program Committee following review of information contained in an abstract submitted by t he author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as prese nted, does not necessarily reflect any position of the Society of Petroleum Engineers,(More)
New upper bounds for the solution of the discrete algebraic Lyapunov equation (DALE) P = APA T + Q are presented. The only restriction on their applicability is that A be stable; there are no restrictions on the singular values of A nor on the diagonalizability of A. The new bounds relate the size of P to the radius of stability of A. The upper bounds are(More)
Recently, B. Roth and M. Woods [7] suggested a reexamination of MCG interpretation through currents transversal to the wave propagation direction. They also gave a formula J'(theta) for the dependence of the current intensity on the angle theta between straight fibers and the plane wave front. Here we study more general situations, including current(More)
Acknowledgements Although this work correctly bears my name as sole author, a thesis is much more than just a text, and cannot be done in isolation. I have been chasing a doctorate for the last seven years, and I got much help along the way. The help I got from the following people and institutions had direct innuence on what I nally wrote down. Jonas de(More)