Fundamental Limitations in Filtering and Control

I Introduction.- 1 A Chronicle of System Design Limitations.- II Limitations in Linear Control.- 2 Review of General Concepts.- 3 SISO Control.- 4 MIMO Control.- 5 Extensions to Periodic Systems.- 6 Extensions to Sampled-Data Systems.- III Limitations in Linear Filtering.- 7 General Concepts.- 8 SISO Filtering.- 9 MIMO Filtering.- 10 Extensions to SISO Prediction.- 11 Extensions to SISO Smoothing.- IV Limitations in Nonlinear Control and Filtering.- 12 Nonlinear Operators.- 13 Nonlinear Control.- 14 Nonlinear Filtering.- A Review of Complex Variable Theory.- A.1 Functions, Domains and Regions.- A.2 Complex Differentiation.- A.3 Analytic functions.- A.3.1 Harmonic Functions.- A.4 Complex Integration.- A.4.1 Curves.- A.4.2 Integrals.- A.5 Main Integral Theorems.- A.5.1 Green's Theorem.- A.5.2 The Cauchy Integral Theorem.- A.5.3 Extensions of Cauchy's Integral Theorem.- A.5.4 The Cauchy Integral Formula.- A.6 The Poisson Integral Formula.- A.6.1 Formula for the Half Plane.- A.6.2 Formula for the Disk.- A.7 Power Series.- A.7.1 Derivatives of Analytic Functions.- A.7.2 Taylor Series.- A.7.3 Laurent Series.- A.8 Singularities.- A.8.1 Isolated Singularities.- A.8.2 Branch Points.- A.9 Integration of Functions with Singularities.- A.9.1 Functions with Isolated Singularities.- A.9.2 Functions with Branch Points.- A. 10 The Maximum Modulus Principle.- A. 11 Entire Functions.- Notes and References.- B Proofs of Some Results in the Chapters.- B.1 Proofs for Chapter 4.- B.2 Proofs for Chapter 6.- B.2.1 Proof of Lemma 6.2.2.- B.2.2 Proof of Lemma 6.2.4.- B.2.3 Proof of Lemma 6.2.5.- C The Laplace Transform of the Prediction Error.- D Least Squares Smoother Sensitivities for Large ?.- References.