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8 1) H. Hausen: Habilitationsschrift, Tech. Hochschule Munchen (1927) Uber die Theorie des Warmeaustausches in Regeneratoren, Z. Angew. Math. Mech., 9-3, 173/200 (1929) 2) W.J.D. van Dijck: U.S. Patent 2, 011, 186 (1935) 4) M.R. Cannon: Controlled Cycling Improves Various Processes, Ind. Eng. Chem., 53-8, 629 (1961) 5) F.M. Magee: The Course of a Reaction in a Chromatographic Column, Ind. Eng. Chem. Fundam., 2-1, 32/36 (1963) 6) R.H. Wilhelm, A.W. Rice and A.R. Bendelius: Parametric Pumping, A Dynamic Principle for Separating Fluid Mixtures, Ind. Eng. Chem. Fundam. 5-1, 141/144 (1966) 7) D.J. Brown (ed.): Proc. 1st International Symp. of Pulse Combustion, Univ. of Sheffield (1971) 8) V.N. Schrodt (chairman): Cyclic Processing Operations, Ind. Eng. Chem. Proc. Des. Dev., 6-1, 2/ 48 (1967) 9) A. Marzollo (ed.): Periodic Optimization, vols I and II, Springer-Verlag (1972) 10) A. Niemi (ed.): Proc. 7th Triennial World Congress of IFAC, 3, 2041/2077 (1978) 11) J. Warga: Relaxed Variational Problems, J. Math. Anal. and Appl., 4-1, 111/128 (1962) 12) M. Fjeld: Quasistationary and High Frequency Periodic Control of Continuous Processes, Proc. IFAC 5th World Congress, Part 3, Paper 33 2, 1/ 7 (1972)

9 13) F.J.M. Horn and R.C. Lin: Periodic Processes, A Variational Approach, Ind. Eng. Chem. Proc. Des. Dev., 6-1, 21/30 (1967) 14) J.E. Bailey: Necessary Conditions for Optimality in a General Class of Non-Linear Mixed Boundary Value Control Problems, Int. J. Control, 16-2, 311/ 320 (1972) 15) S. Bittanti, G. Fronza, G. Guardabassi and C. Maffezzoni: A Maximum Principle for Periodic Optimization, Richerche di Automatica, 3-2, 170/ 179 (1972) 31) N. Y. Gaitonde and J.M. Douglas: The Use of Positive Feedback Control Systems to Improve Reactor Performance, AIChE J., 15-6, 902/910 (1969) 32) M. Matsubara and K. Onogi: Stabilized Suboptimal Periodic Control of a Chemical Reactor, IEEE Trans. Automat. Contr. AC-23-6, 1005/1008 (1978) 33) M. Matsubara and K. Onogi: Unstable Suboptimal Periodic Control of a Ceratin Chemical Reactor, ibid., 1111/1113 (1978) 34) K. Onogi and M. Matsubara: Point-Transformation Analysis of Relay Control Systems, IEEE Trans, Automat. Contr., AC-24-5, 730/735 (1979) 17) M. Matsubara, Y. Nishimura and N. Takahashi: 35) J.-S. Liaw and J.E. Bailey: Regulation of Lumped Optimal Periodic Control of Lumped Parameter Periodic Processes, AIChE J., 20-5, 924/932 (1974) Systems, JOTA, 13-1, 13/31 (1974) 36) E.B. Dale and I.A. Furzer: Periodic Cycling of 18) E.G. Gilbert: Optimal Periodic Control: A General Plate Columns-Control Simulations and Experiments, Chem. Eng. Sci., 33-7, 905/911 (1978) Theory of Necessary Conditions, SIAM J. Control and Optimization, 15-5, 717/746 (1977) 37) D. Sincic and J.E. Bailey: Pathological Dynamic 19) E.G. Gilbert: Optimal Periodic Control: A Solution Behavior of Forced Periodic Chemical Processes, Set Theory of Necessary and Sufficient Conditions, Chem. Eng. Sci., 32-3, 281/286 (1977) Proc. 7th Triennial World Congress of IFAC, 3, 38) M. Matsubara and K. Onogi: Structure Analysis 2057/2064 (1978) of Periodically Controlled Nonlinear Systems via 20) J.E. Bailey and F.J.M. Horn: Comparison between the Stroboscopic Approach. IEEE Trans. Automat Two Sufficient Conditions for Improvement of an Contr., AC-22-4, 678/680 (1977) Optimal Steady-State Process by Periodic Optimization, JOTA, 7-5, 378/384 (1971) of Periodically Controlled Chemical Processes, 39) K. Onogi and M. Matsubara: Structure Analysis 21) S. Bittanti, G. Fronza and G. Guardabassi: Perio Chem. Eng. Sci., 35-5, 1009/1019 (1980) dic Control: A Frequency Domain Approach, 40) R.A. Gaska and M.R. Cannon: Controlled Cycling IEEE Trans. Automat. Contr., AC-18-1, 33/38 Distillation in Sieve and Screen Plate Towers, (1973) Ind. Eng. Chem., 53-8, 630/631 (1961) 22) G. Guardabassi and N. Schiavoni: Boundary 41) V.N. Schrodt, J.T. Sommerfeld, O.R. Martin, P. Optimal Constant Control versus Periodic Operation, Proc. IFAC 6th World Congress, Part 1, Controlled Cyclic Distillation, Chem. Eng. Sci., 22- E. Parisot and H.H. Chien: Plant-Scale Study of Paper 22.2, 1/6 (1975) 5, 759/767 (1967) 42) G. Baron and S. Wajc: Periodic Distillation in a Horizontal Column, I. Chem. E. Symp. Series, No. 56. Paper /44 (1979) 24) N. Watanabe, Y. Nishimura and M. Matsubara: Singular Control Test for Optimal Periodic Control Problems, IEEE Trans. Automat Contr., AC- 21-4, 609/610 (1976) 25) H.M. Robins: A Generalized Legendre-Clebsch Condition for the Singular Classes of Optimal Control, IBM J. of Research and Development, 11-4, 361/372 (1967) 46) E.G. Gilbert: Vehicle Cruise: Improved Fuel Economy by Periodic Control, Automatica, 12-2, 159/ 26) M. Matsubara, Y. Nishimura, N. Watanabe and K. Shimizu: Periodic Control of Continuous Distillation Processes, Chem. Eng. Sci., 30-9, 1075/ 47) W.R. Emanuel and R.L. Mulholland: Linear Per- 166 (1976) 1083 (1975) iodic Control with Applications to Environmental 27) M. Matsubara, Y. Nishimura and N. Watanabe: Systems, Int. J. Control. 24-6, 807/820 (1976) Application of the Singular Control Test to Periodic Control Problems of a Continuous Distillation Process, Int. J. Control, 22-6, 773/785 (1975) 28) M. Matsubara, Y. Nishimura and N. Takahashi: 49) J.E. Bailey: Periodic Operation of Chemical Reactors; A Review, Chem. Eng. Commun., 1-3, 111/ Periodic Operation of CSTR-I Idealized Control, Chem. Eng. Sci., 28-7, 1369/1377 (1973) 124 (1974) 29) ibid.-ii Practical Control, Chem. Eng. Sci., 28-7, 50) G. Guardabassi, A. Locatelli and S. Rinaldi: Status 1379/1385 (1973) of Periodic Optimization of Dynamical Systems, 30) N. Watanabe, K. Onogi and M. Matsubara: Periodic Control of Continuous Stirred Tank Reactors- JOTA, 14-1, 1/20 (1974) I The Pi Criterion and Its Applications to Isothermal Cases, Chem. Eng. Sci. 36-5, 809/818 (1981)

(1970) 17) V. Kucera: A Contribution to Matrix Ouadratic Equations, IEEE Trans. on Automatic Control, AC- 17-3, 344/347 (1972) 18) V. Kucera: On Nonnegative Definite Solutions to Matrix Ouadratic Equations,

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