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. Language: English