High gain control of Stochastic Differential Equations | Analytical and Numerical methods for the calculation of moment exponents and rotation numbers

Iakovos Matsikis

ISBN 10: 3838366530 / ISBN 13: 9783838366531

Published by LAP LAMBERT Academic Publishing, 2010

About this Item

High gain control of Stochastic Differential Equations | Analytical and Numerical methods for the calculation of moment exponents and rotation numbers | Iakovos Matsikis | Taschenbuch | 156 S. | Englisch | 2010 | LAP LAMBERT Academic Publishing | EAN 9783838366531 | Verantwortliche Person für die EU: BoD - Books on Demand, In de Tarpen 42, 22848 Norderstedt, info[at]bod[dot]de | Anbieter: preigu.

Seller Inventory # 101095364

Bibliographic Details

• Title: High gain control of Stochastic Differential Equations | Analytical and Numerical methods for the calculation of moment exponents and rotation numbers
• Publisher: LAP LAMBERT Academic Publishing
• Publication Date: 2010
• Language: English
• ISBN 10: 3838366530
• ISBN 13: 9783838366531
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 220W x 150H x 10D millimeters 220 millimeters width by 150 millimeters height by 10 millimeters depth
• Weight: 250 grams
• Seller catalogs:
  • Bücher

About this title

Synopsis

This work tries to address the problem of assessing the long term dynamics of control systems described by linear, stochastic, differential equations upon application of high gain, proportional, output feedback. Stability of such stochastic systems is characterized by moment exponents and rotation numbers. We present two analytical techniques to determine mean or else almost sure stability and rotation in state space. The first is projection onto the unit sphere, derivation of the associated Fokker-Planck equation on projective space and finally computation of mean exponents and rotation numbers, the stochastic equivalents of the real and imaginary parts of eigenvalues, by using ergodic arguments that allow passing from time to space averages. The second is an expansion technique based on a perturbation analysis of the generator that defines the diffusion. As an alternative or compliment to mean stability we discuss furthermore second mean stabilization and a linear algebraic technique with roots in control theory for calculating second mean exponents.