Series Preface
Preface
Figures
0 Introduction
0.1 System representations
0.1.1 Block diagrams
0.1.2 Nonlinear equations and linear decompositions
0.2 R,obust control problems and uncertainty
0.2.1 Stabilization
0.2.2 Disturbances and commands
0.2.3 Unmodeled dynamics
Notes and references
1 Preliminaries in Finite Dimensional Space
1.1 Linear spaces and mappings
1.1.1 Vector spaces
1.1.2 Subspaces
1.1.3 Bases, 8pans, and linear independence
1.1.4 Mappings and matrix representations
1.1.5 Change of basis and invariance
1.2 Subsets and convexity
1.2.1 Some basic topology
1.2.2 Convex sets
1.3 Matrixtheory
1.3.1 Eigenvalues and Jordan form
1.3.2 Self-adjoint, unitary, and positive definite matrices
1.3.3 Singular value decomposition
1.4 Linear matrix inequalities
Exercises
Notes and references
2 State Space System Theory
2.1 The autonomous system
2.2 Controllability
2.2.1 Reachability
2.2.2 Properties of controllability
2.2.3 Stabilizability...
2.2.4 Controllability from a single input
2.3 Eigenvalue assignment
2.3.1 Single-input case
2.3.2 Multi-input case
2.4 Observability...
2,4.1 The unobservable subspace
2.4.2 Observers
2.4.3 Observer-based Controllers
2.5 Minimal realizations
2.6 Transfer functions and state space
2.6.1 R,ational matrices and state space realizations
2.6.2 Minimality
Exercises
Notes and references
3 Linear Analysis
3.1 Normed and inner product spaces
3.1.1 Complete spaces
3.2 Operators
3.2.1 Banach algebras
3.2.2 Some elements of spectral theory
3.2.3 Adjoint operators in Hilbert space
3.3 Frequency domain spaces: Signals
3.3.1 The space 2 and the Fourier transform
3.3.2 The spaces H2 and H21 and the Laplace transform
3.3.3 Summarizing the big picture
3.4 Frequency domain spaces: Operators
3.4.1 Time invariance and multiplication operators
3.4.2 Causality with time invariance
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