Mathematical Control Theory - Springer Nature B.V - Hardcover - en Book

1 Path Integrals And Stability.- 1.1 Introduction.- 1.2 Path Independence.- 1.3 Positivity Of Quadratic Differential Forms.- 1.4 Lyapunov Theory For High-order Differential Equations.- 1.5 The Bezoutian.- 1.5.1 The Routh Test.- 1.5.2 The Kharitonov Theorem.- 1.6 Dissipative Systems.- 1.7 Stability Of Nonautonomous Systems.- 1.8 Conclusions.- 1.9 Appendixes.- 1.9.1 Appendix A: Notation.- 1.9.2 Appendix B: Linear Differential Systems.- 1.9.3 Appendix C: Proofs.- 2 The Estimation Algebra Of Nonlinear Filtering Systems.- 2.1 Introduction.- 2.2 The Filtering Model And Background.- 2.3 Starting From The Beginning.- 2.4 Early Results On The Homomorphism Principle.- 2.5 Automorphisms That Preserve Estimation Algebras.- 2.6 Bm Estimation Algebra.- 2.7 Structure Of Exact Estimation Algebra.- 2.8 Structure Of Bm Estimation Algebras.- 2.9 Connection With Metaplectic Groups.- 2.10 Wei-norman Representation Of Filters.- 2.11 Perturbation Algebra And Estimation Algebra.- 2.12 Lie-algebraic Classification Of Maximal Rank Estimation Algebras.- 2.13 Complete Characterization Of Finite-dimensional Estimation Algebras.- 2.14 Estimation Algebra Of The Identification Problem.- 2.15 Solutions To The Riccati P.d.e.- 2.16 Filters With Non-gaussian Initial Conditions.- 2.17 Back To The Beginning.- 2.18 Acknowledgement.- 3 Feedback Linearization.- 3.1 Introduction.- 3.2 Linearization Of A Smooth Vector Field.- 3.3 Linearization Of A Smooth Control System By Change-of-state Coordinates.- 3.4 Feedback Linearization.- 3.5 Input-output Linearization.- 3.6 Approximate Feedback Linearization.- 3.7 Normal Forms Of Control Systems.- 3.8 Observers With Linearizable Error Dynamics.- 3.9 Nonlinear Regulation And Model Matching.- 3.10 Backstepping.- 3.11 Feedback Linearization And System Inversion.- 3.12 Conclusion.- 4 On The Global Analysis Of Linear Systems.- 4.1 Introduction.- 4.2 The Geometry Of Rational Functions.- 4.2.1 Spaces Of Scalar-inputscalar-output Linear Systems.- 4.2.2 The Deterministic Pa