Stabilization of companion form systems by mean zero noise

Abstract

It is shown that the Lyapunov exponents of a linear system with companion form d x d-matrix can be squeezed into an arbitrarily small neighborhood of trace A/d by means of mean zero degenerate real noise or a combination of real and white noise. In particular, the damped inverse pendulum can be stabilized by such a noise. The proof includes a random transformation of the coordinate system and a stochastic averaging principle.

Keywords:

• Lyapunov exponents
• Stability
• Stabilization by noise
• Stochastic linear systems
• Companion form matrix
• AMS Classification: 60H10, 93E15

Research supported in part by NSF grant#9017702

Research supported in part by NSF grant#9017702

Notes

Research supported in part by NSF grant#9017702