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Controllability, Stabilization, and the Regulator Problem for Random Differential Systems
Russell Johnson, University of Florence, Italy, and Mahesh Nerurkar, Rutgers University, Camden, NJ

Memoirs of the American Mathematical Society
1998; 48 pp; softcover
Volume: 136
ISBN-10: 0-8218-0865-6
ISBN-13: 978-0-8218-0865-8
List Price: US$44
Individual Members: US$26.40
Institutional Members: US$35.20
Order Code: MEMO/136/646
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This volume develops a systematic study of time-dependent control processes. The basic problem of null controllability of linear systems is first considered. Using methods of ergodic theory and topological dynamics, general local null controllability criteria are given. Then the subtle question of global null controllability is studied. Next, the random linear feedback and stabilization problem is posed and solved. Using concepts of exponential dichotomy and rotation number for linear Hamiltonian systems, a solution of the Riccati equation is obtained which has extremely good robustness properties and which also preserves all the smoothness and recurrence properties of the coefficients. Finally, a general version of the local nonlinear feedback stabilization problem is solved.


Graduate students and research mathematicians working in dynamical systems.

Table of Contents

  • Introduction
  • Basic dynamical notions
  • Random linear control processes
  • Some facts about random linear systems
  • Sufficiency conditions for uniform controllability
  • Dependence of controllability on the dynamics of the flow
  • Global null controllability
  • The feedback stabilization problem for random linear systems
  • The rotation number
  • The solution of the linear regulator and the stabilization problem
  • Linearization of the regulator and the stabilization problem
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