Geometric Systems Theory

Note: The links do not work, but you can download the first chapters from here

Contents

• Preface
• Introduction
• Invariant and controlled invariant subspaces
  • Invariant subspaces
  • Controlled invariant subspaces
  • Reachability subspaces
  • Representation of systems in special bases
  • Maximal reachability subspaces
  • Reachability under state constraints
• The disturbance decoupling problem (DDP)
  • Geometric formulation
  • Computing V*
  • Disturbance decoupling, observability, and zeros
  • Disturbance decoupling with eigenvalue assignment
  • Solution of the DDPP
• Zeros and zero dynamics
  • Zero dynamics for SISO systems
  • Zero dynamics of MIMO systems
  • Zeros and system inversion
  • An illustration of zero dynamics: high gain control
• Noninteracting control and tracking
  • Problem formulation
  • Tracking with stability
• Input-output behavior
  • State observation
  • Output tracking input
  • The partial stochastic realization problem
• Output regulation and internal model principal
  • Full information output regulation
  • Error feedback output regulation
  • Output regulation and zero dynamics
• Nonlinear systems
  • Introduction
  • Controllability
    • Some Mathematical Preparations
    • Nonlinear Controllability and Accessibility
  • Stability of nonlinear systems
  • Steady state response and center manifold
  • Center manifold theory
  • Disturbance decoupling problem (DDP)
  • Exact linearization via feedback
  • Zero dynamics and its applications
  • Limitation of high gain control
• Numerical aspects in geometric control theory
  • Introduction
  • Representation of linear model
    • Scaling
  • The singular value decomposition
    • The numerical rank of a matrix
    • Calculus of subspaces
  • A list of useful MATLAB commands
• Exercises on Geometric Control Theory
• References
• Index