Memoirs of the American Mathematical Society 1998; 48 pp; softcover Volume: 136 ISBN10: 0821808656 ISBN13: 9780821808658 List Price: US$44 Individual Members: US$26.40 Institutional Members: US$35.20 Order Code: MEMO/136/646
 This volume develops a systematic study of timedependent 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. Readership 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
