N., On the solvability of matrix inequalities, Mat. Zametki 36 1984, 725– Boundary control systems, SIAM J. Control Optim. 6 1968, 349–385.

On the solutions 131 References [1] B ALAKRISHNAN A. V., On a generalization of the Kalman-Yakubovich Lemma, Appl. Math. Optim. 31 1995, 177–187. [2] C HURILOV

A. N., On the solvability of matrix inequalities, Mat. Zametki 36 1984, 725–

732. [3] D ESCH W., L ASIECKA I., S CHAPPACHER W., Feedback boundary control problems for linear semigroups, Israel J. of Mathematics 51 1985, 177–207. [4] F ATTORINI

O., Boundary control systems, SIAM J. Control Optim. 6 1968, 349–385.

[5] G ARNETT J. B., Bounded Analytic Functions, Academic Press, New York 1981. [6] L ASIECKA I., T RIGGIANI R., Differential and Algebraic Riccati Equations with Applica- tions to BoundaryPoint Control Problems: Continuous Theory and Approximation Theory, Lect. Notes in Control Inf. Sci. n. 164, Springer-Verlag, Berlin 1991. [7] L OUIS J-C L ., W EXLER D., The Hilbert space regulator problem and operator Riccati equation under stabilizability, Ann. Soc. Sci. Bruxelles S´er I 105 1991, 137–165. [8] P ANDOLFI L., From singular to regular control systems, in “Control of Partial Differential Equations”, G. Da Prato and M. Tubaro Ed.s, M. Dekker, New York 1994, 153–165. [9] P ANDOLFI L., Dissipativity and the Lur’e Problem for parabolic boundary control sys- tems, SIAM J. Control Optimization 36 1998, 2061–2081. [10] P ANDOLFI L., The standard regulator problem for systems with input delays: an approach through singular control theory, Appl. Math. Optim. 31 1995, 119–136. [11] P ANDOLFI L., The Kalman–Yakubovich–Popov Theorem for stabilizable hyperbolic boundary control systems, Integral Equations Operator Theory, to appear. [12] P OPOV V. M., Absolute stability of nonlinear systems of automatic control, Automat. Re- mote Control 22 1961, 857–875. [13] R OSENBLUM M., R OVNYAK J., Topics in Hardy classes and univalent functions, Birk¨auser Verlag, Basel 1994. [14] Y AKUBOVICH

V. A., The frequency theorem in control theory, Siberian Math. J. 14 1973,

384–419. AMS Subject Classification: ???. L. PANDOLFI Politecnico di Torino Dipartimento di Matematica Corso Duca degli Abruzzi, 24 10129 Torino, Italy e-mail: ✟ ✆ ✁ ✄ ✝ ✞ ✁ ✁ ✆ ☞ ✁ ✡ ✆ ☞ 132 L. Pandolfi Rend. Sem. Mat. Univ. Pol. Torino Vol. 56, 4 1998

F. Rampazzo – C. Sartori ON PERTURBATIONS OF MINIMUM PROBLEMS