This short paper presents an hyperstability theorem for hybrid dynamic systems composed of coupled differential and difference equations subject to time varying nonlinearities satisfying a Popov ' s type inequality . Some corollaries and related physical interpretations are also given.

Recently Callan, Giddings, Harvey and the author derived a set of one-loop semiclassical equations describing black hole formation/evaporation in two-dimensional dilaton gravity conformally coupled to N scalar fields. These equations were subsequently used to show that an incoming matter wave develops a black hole type singularity at a critical value φ cr of the dilaton field. In this paper a m...

with the condition that an, bm 6= 0 as other wise the polynomials would be of a lower degree than claimed. We will also want to impose that one of a0, b0 is no zero, if they were both zero then the two polynomials would have a common zero at z = 0 and thus would not be co-prime. We also need to mention that both P and Q are not the zero polynomial. If P is the zero polynomial then R is the cons...

In this paper we extend the classical Lefschetz version of the KalmanYacubovich-Popov (KYP) lemma to the case of matrices with general regular inertia. We then use this result to derive an easily verifiable spectral condition for a pair of matrices with the same regular inertia to have a common Lyapunov solution (CLS), extending a recent result on CLS existence for pairs of Hurwitz matrices.

Abstruct-The purpose of this paper is to demonstrate robust compensators designed using Popov controller synthesis on the Middeck Active Control Experiment (MACE): a Shuttle program scheduled for flight in January, 1995. The experiment has been designed to investigate the extent to which the on-orbit behavior of a precision-controlled spacecraft can be predicted and controlled using analysis an...