Periodic Feedback Stabilization for Linear Periodic Evolution Equations

By Gengshen Wang and Yashan Xu

1 Controlled Periodic Equations, LQ Problems and Periodic Stabilization. 1.1 Controlled Periodic Evolution Equations. 1.2 Linear Quadratic Optimal Control Problems. 1.2.1 Finite horizon case. 1.2.2 Infinite horizon case. 1.3 Relation between Periodic Stabilization and LQ Problems. 2 Criteria on Periodic Stabilization in Infinite Dimensional Cases. 2.1 Attainable Subspaces. 2.2 Three Criterions on Periodic Feedback Stabilization. 2.2.1 Multi-periodic feedback stabilization. 2.2.2 Proof of Theorem 2.1. 2.3 Applications2.3.1 Feedback realization in finite dimensional subspaces. 2.3.2 Applications to heat equations. 3 Criteria on Periodic Stabilization in Finite Dimensional Cases. 3.1 Null Controllable Subspaces. 3.2 Algebraic Criterion and Application. 3.2.1 The proof of (a), (c) in Theorem 3.1. 3.2.2 The proof of (a), (b) in Theorem 3.1. 3.2.3 Decay rate of stabilized equations. 3.3 Geometric Criterion. 4 Design of Simple Control Machines. 4.1 The First Kind of Simple Control Machines. 4.2 The Second Kind of Simple Control Machines-General Case. 4.3 The Second Kind of Simple Control Machines-Special Case

• Format: Paperback
• Language: English
• ISBN: 3319492373
• ISBN13: 9783319492377
• Release Date: February 2017
• Publisher: Springer
• Length: 127 Pages
• Weight: 0.45 lbs.
• Dimensions: 0.3" x 6.1" x 9.2"