Szegö: An application of the extension theorem to a control problem

Szegö, Giorgio P.:
An application of the extension theorem to a control problem
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Serie 8 42 (1967), fasc. n.6, p. 766-770, (English)
pdf (441 Kb), djvu (578 Kb). | MR 0230999 | Zbl 0183.16301

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In questo lavoro si studia il problema della stabilità assoluta di un sistema di controllo non lineare sotto opportune ipotesi sulla nonlinearità e la sua derivata prima. Mediante l'uso del teorema di estensione e di una funzione di Liapunov di nuovo tipo si ricavano condizioni sufficienti per la stabilità assoluta.

Referenze Bibliografiche

[1] N. P. BHATIA and G. P. SZEGÖ, An extension theorem for asymptotic stability and its applications to a control problem, in Proc. International Symposium on Diff. Equations and Dynamical Systems, Puerto Rico (1965). | MR 230991

[2] G. P. SZEGÖ, New theorems on stability and attraction and their application to a control problem, in Proc. NATO Advanced Study Institute on Stability Problems of solutions of Differential Equations, Padua, Sept. 1965, published by Oderisi, Gubbio (1966). | MR 417901

[3] N. P. BHATIA and G. P. SZEGÖ, Dynamical Systems: Stability theory and application, Lecture Notes in Mathematics, Springer-Verlag, Berlin-Heidelberg-New York (1967). | MR 219843 | Zbl 0155.42201

[4] V. M. POPOV, Hiperstabilitatea Sistemelor Automate, Editura Academiei Republicii Socialiste Romania, Bucarest (1966). | MR 387747

[5] C. CORDUNEANU, Sur une équation intégrale non-linéaire, «Anal. Sti. Unit. “A. Cuza”, Iasi», Sct. 1, 9, 369-375 (1963). | MR 184053 | Zbl 0173.40102

[6] V. A. IAKUBOVICH, Frequency-domain condition of asymptotical stability of nonlinear control systems, in Proc. Joint Conference on Application of Stability Theory and Analytical Mechanics, Kazan (1964).

[7] K. S. NARENDRA and C. P. NEUMANN, Stability of a Class of Differential Equations with a Single Monotone Increasing Nonlinearity, in Tech. Rept. 497 (1965), Cruft Lab., Harvard University, Cambridge, Mass. | MR 204176

[8] A. I. LUR'E, Some Nonlinear Problems in the Theory of Automatic Control, Moscow (1951). | MR 60677

[9] V. A. IAKUBOVICH, The Solution of Certain Matrix Inequalities Encountered in the Theory of Automatic Control, «D.A.N. SSSR», 143 (1962). | MR 133333

[10] R. E. KALMAN, Liapunov Functions for the Problem of Lur'e in Automatic Control, «Proc. Nat. Acad. Sci. U.S.», 49 (1963). | fulltext (doi) | MR 151696 | Zbl 0113.07701

[11] G. P. SZEGÖ, Asymptotic Behavior of Time-varying, Forced, Non—linear Control Systems, to appear. | MR 386811

[12] K. S. NARENDRA and C. P. NEUMANN, Stability of a Class of Differential Equations with a Single Nonlinearity, in Tech. Rept. 468 (1965). Cruft Lab., Harvard University, Cambridge, Mass. | MR 204176

[13] V. I. ZUBOV, Methods of A. M. Liapunov and their application, Noordhoff, Groningen, Holland (1964). | MR 179428

[14] P. HARTMAN, Ordinary Differential Equations, New York, New York (1964). | MR 171038 | Zbl 0125.32102

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Referenza completa

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Referenze Bibliografiche