H -Control Theory: Lectures given at the 2nd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Como, Italy, June 18-26, 1990 (Lecture Notes in Mathematics, 1496)

The fundamental problem in control engineering is to provide robust performance to uncertain plants. H -control theory began in the early eighties as an attempt to lay down rigorous foundations on the classical robust control requirements. It now turns out that H -control theory is at the crossroads of several important directions of research space or polynomial approach to control and classical interpolation theory; harmonic analysis and operator theory; minimax LQ stochastic control and integral equations. The book presents the underlying fundamental ideas, problems and advances through the pen of leading contributors to the field, for graduate students and researchers in both engineering and mathematics. From the Contents: C. Foias: Commutant Lifting Techniques for Computing Optimal H Controllers.- B.A. Francis: Lectures on H Control and Sampled-Data Systems.- J.W. Helton: Two Topics in Systems Engineering Frequency Domain Design and Nonlinear System.- H. Kwakernaak: The Polynomial Approach to H -Optimal Regulation.- J.B. Pearson: A Short Course in l - Optimal Control Commutant Lifting Techniques For Computing Optimal H-controllers / C. Foias -- Lectures On H-control And Sampled-data Systems / B.a. Francis -- Two Topics In Systems Engineering Frequency Domain Design And Nonlinear Systems / J.w. Helton -- The Polynomial Approach To H-optimal Regulation / H. Kwakernaak -- A Short Course In L1-optimal Control / J.b. Pearson -- On The Hamiltonian Structure In The Computation Of Singular Values For A Class Of Hankel Operators / P.a. Fuhrmann -- Nehari Interpolation Problem For Rational Matrix Functions : The Generic Case / J.a. Ball, I. Gohberg, L. Rodman -- Time Variant Extension Problems Of Nehari Type And The Band Method / I. Gohberg, M.a. Kaashoek, H.j. Woerdeman. C. Foiaş ... [et Al.] ; Editors, E. Mosca, L. Pandolfi. On T.p. [infinity] Appears As The Infinity Symbol. Includes Bibliographical References. Commutant lifting techniques for computing optimal H ∞ controllers....Pages 1-36 Lectures on H ∞ control and sampled-data systems....Pages 37-105 Two topics in systems engineering: Frequency domain design and nonlinear systems....Pages 106-140 The polynomial approach to H ∞ -optimal regulation....Pages 141-221 Notes on l 1 -optimal control....Pages 222-249 On the hamiltonian structure in the computation of singular values for a class of Hankel operators....Pages 250-276 Nehari interpolation problem for rational matrix functions: The generic case....Pages 277-308 Time variant extension problems of Nehari type and the band method....Pages 309-323