Author | Sontag, Eduardo D. author |
---|---|
Title | Mathematical Control Theory [electronic resource] : Deterministic Finite Dimensional Systems / by Eduardo D. Sontag |
Imprint | New York, NY : Springer US, 1990 |
Connect to | http://dx.doi.org/10.1007/978-1-4684-0374-9 |
Descript | XIII, 396 p. online resource |
1 Introduction -- 1.1 What Is Mathematical Control Theory? -- 1.2 Proportional-Derivative Control -- 1.3 Digital Control -- 1.4 Feedback Versus Precomputed Control -- 1.5 State-Space and Spectrum Assignment -- 1.6 Outputs and Dynamic Feedback -- 1.7 Dealing with Nonlinearity -- 1.8 A Brief Historical Background -- 1.9 Some Topics Not Covered -- 2 Systems -- 2.1 Basic Definitions -- 2.2 I/O Behaviors -- 2.3 Discrete-Time -- 2.4 Linear Discrete-Time Systems -- 2.5 Smooth Discrete-Time Systems -- 2.6 Continuous-Time -- 2.7 Linear Continuous-Time Systems -- 2.8 Linearizations Compute Differentials -- 2.9 More on Differentiability* -- 2.10 Sampling -- 2.11 Volterra Expansions* -- 2.12 Notes and Comments -- 3 Reachability and Controllability -- 3.1 Basic Reachability Notions -- 3.2 Time-Invariant Systems -- 3.3 Controllable Pairs of Matrices -- 3.4 Controllability Under Sampling -- 3.5 More on Linear Controllability -- 3.6 First-Order Local Controllability -- 3.7 Piecewise Constant Controls -- 3.8 Notes and Comments -- 4 Feedback and Stabilization -- 4.1 Constant Linear Feedback -- 4.2 Feedback Equivalence* -- 4.3 Disturbance Rejection and Invariance* -- 4.4 Stability and Other Asymptotic Notions -- 4.5 Unstable and Stable Modes* -- 4.6 Lyapunovโs Direct Method -- 4.7 Linearization Principle for Stability -- 4.8 More on Smooth Stabilizability* -- 4.9 Notes and Comments -- 5 Outputs -- 5.1 Basic Observability Notions -- 5.2 Time-Invariant Systems -- 5.3 Continuous-Time Linear Systems -- 5.4 Linearization Principle for Observability -- 5.5 Realization Theory for Linear Systems -- 5.6 Recursion and Partial Realization -- 5.7 Rationality and Realizability -- 5.8 Abstract Realization Theory* -- 5.9 Notes and Comments -- 6 Observers and Dynamic Feedback -- 6.1 Observers and Detectability -- 6.2 Dynamic Feedback -- 6.3 External Stability for Linear Systems -- 6.4 Frequency-Domain Considerations -- 6.5 Parameterization of Stabilizers -- 6.6 Notes and Comments -- 7 Optimal Control -- 7.1 An Optimal Control Problem -- 7.2 Dynamic Programming -- 7.3 The Continuous-Time Case -- 7.4 Linear Systems with Quadratic Cost -- 7.5 Infinite-Time Problems -- 7.6 Tracking -- 7.7 (Deterministic) Kalman Filtering -- 7.8 Notes and Comments -- Appendixes -- A Linear Algebra -- A.1 Operator Norms -- A.2 Singular Values -- A.3 Jordan Forms and Matrix Functions -- A.4 Continuity of Eigenvalues -- B Differentials -- B.1 Finite Dimensional Mappings -- B.2 Maps Between Normed Spaces -- C Ordinary Differential Equations -- C.1 Review of Lebesgue Measure Theory -- C.2 Initial-Value Problems -- C.3 Existence and Uniqueness Theorem -- C.4 Continuous Dependence -- C.5 Linear Differential Equations -- C.6 Stability of Linear Equations