Generalized aspects of Riccati equation focused on the roles of its solution in control problem

  • Dong, Tian (Institute of Engineering Mechanics, University of Tsukuba) ;
  • Michio, Ohta (Institute of Engineering Mechanics, University of Tsukuba)
  • Published : 1994.10.01

Abstract

It is well known that the Boyd's theorem states the relation between the imaginary eigenvalues of discriminant H of Riccati equation (A, R, Q) and the singular value of transfer function, but it is only available for R .geq. 0 and Q .geq. 0. In this paper, we extend Boyd's theorem for two case, that is, R is symmetric, Q is sign definite, and R is sign definite, Q is symmetric. We give under the condition that there is a real symmetric solution of Riccati equation the relation between H has imaginary eigenvalue and the maximum eigenvalue of transfer functoin. Finally, we give a necessary and sufficient condition to determine whether H has imaginary eigenvalue under some conditions.

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