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Nonlinear H-Infinity Control

Singular information state dynamics
2-D hyperbolic

In this animated image we see the information state evolving as a function of time. You will notice that it collapses onto a vertical plane as time progresses, illustrating convergence to the singular equilibrium information state

from an initial finite-valued initial condition. Here, M_as is the antistable manifold - a line in this animation - of a certain vector field and p-breve is a finite-valued function on this manifold. This equilibrium is a (local) attractor for the information state dynamical system. (In linear H-infinity control theory, this corresponds to the stabilizing solution Y of the filter-type algebraic Riccati equation (which has a one dimensional null space in this case).)