Research interests
 Supported projects since  2007
 Supported projects
 (1994 - 2006)
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  The Kalman-Yakubovich-Popov Theorem in thermo-elastic problems

The Kalman-Yakubovich-Popov Theorem for infinite-dimensional systems: Some new results

a) Bounded control operator, C0-semigroups, Pritchard-Salamon systems
  • Louis, J. Cl. and D. Wexler: The Hilbert space regulator problem and operator Riccati equation under stabilizability. Ann. Soc. Sci. Bruxelles, Ser. 1, 105, 1991, 137 -- 165.
  • Van Keulen, B.: Equivalent conditions for the solvability of the nonstandard LQ-problem for Pritchard-Salamon systems. J. Control Optim., 33, 1995, 1326 -- 1356.
  • Curtain, R. F.: The Kalman-Yakubovich-Popov Lemma for Pritchard-Salamon systems. System & Control Lett., 27, 1996, 67 -- 72.
  • Curtain, R. F. and J. C. Oostveen: The Popov criterion for strongly stable distributed parameter systems. Int. J. Control, 74 (3), 2001, 265 -- 280.

b) Parabolic systems, holomorphic semigroups, heat equation
  • Pandolfi, L.: Dissipativity and Lur'e problem for parabolic boundary control systems. SIAM J. Control Optimiz., 36, 1998, 2061 -- 2081.
  • Bucci, F.: Frequency domain stability of nonlinear feedback systems with unbounded input operator. Dynamics of Continuous, Discrete and Impulsive Systems, 7, 2000, 351 -- 368.

c) First order hyperbolic equations
  • Triggiani, R.: An optimal control problem with unbounded control operator and unbounded observation operator where the algebraic Riccati equation is satisfied as a Lyapunov equation. Appl. Math. Lett., 10 (2), 1997, 95 -- 102.

d) Second order hyperbolic systems, Euler-Bernoulli equation, Kirchhoff equation, Schrödinger equation, string and membrane equation
  • Lasiecka, I. and R. Triggiani: Algebraic Riccati equations arising in boundary / point control: A review of theoretical and numerical results. In: Perspective in control theory, Jacubczyk, B., Malanowski, K., Raspondek, W. eds., Birkhäuser, Boston, 1990. Part 1: Continuous case, 175 -- 210; Part 2: Approximation theory, 211 -- 235.
  • Bucci, F.: The non-standard LQR problem for boundary control systems. Rend. Sem. Mat. Univ. Pol. Torino, 56 (4), 1998, 105 -- 114.
  • Pandolfi, L.: The Kalman-Yakubovich-Popov Theorem for stabilizable hyperbolic boundary control systems. Integral Equations Operator Theory, 34, 1999, 478 -- 493.
  • Barbu, V., Lasiecka, I. and R. Triggiani: Extended algebraic Riccati equations in the abstract hyperbolic case. Nonlinear. Anal. 40, 2000, 105 -- 129.

e) Nonstandard Riccati equations arising in boundary control problems governed by damped wave and plate equations; Hammerstein integral equations with weekly singular kernels
  • Flandoli, F.: Riccati equations arising in a boundary control problem with distributed parameters. SIAM Journal on Control and Optimization, 22, 1984, 76 -- 86.
  • Lasiecka, I., D. Lukas and L. Pandolfi: Input dynamics and nonstandard Riccati equations with applications to boundary control of damped wave and plate equations. Journal of Optimization Theory and Applications, 84 (3), 1995, 549 -- 574.

f) Discrete time distributed systems, approximation theory for boundary control systems
  • Helton, J. W.: A spectral factorization approach to the distributed stable regulator problem; the algebraic Riccati equation. SIAM Journal on Control and Optimization, 14, 1976, 639 -- 661.
  • Malinen, J.: Discrete time H^\infty algebraic Riccati equations. Techn. Report A 428, Institute of Mathematics, Helsinki University, Finland, 2000.
  • Arov, D. Z., Kaashoek, M. A., and D. R. Pik: The Kalman-Yakubovich-Popov inequality and infinite dimensional discrete time dissipative systems. J. Operator Theory, 2005, to appear.

g) Generalized (possibly unbounded) solutions of the KYP inequality
  • Arov, D. Z. and O. J. Staffans: The infinite-dimensional continuous time Kalman-Yakubovich-Popov inequality. Operator Theory: Advances and Applications, 1, 2005, Birkhäuser Verlag Basel, 1 -- 28.

h) Overview articles
  • Pandolfi, L.: The Kalman-Popov-Yakubovich Theorem: an overview and new results for hyperbolic control systems. Nonlinear Analysis, Methods & Applications, 30 (2), 1997, 735 -- 745.
  • Pandolfi, L.: Recent results on the Kalman-Popov-Yakubovich problem. Proc. Int. Conf. on Mathematics and its Applications, Yagyarta, 1999.