Bounded real transfer functions and G-contractive solutions of matrix Riccati differential equations

Bounded real systems that represent an energy dissipating system are considered. A mutual relationship between these systems and algebraic Ricatti equations is established. The relationship helps clarify the fundamental role that structural properties impart to the qualitative behavior of the algebraic Ricatti equations. Strictly bounded real systems ensure that the general solutions of the algebraic Riccati equation are contractive, which means that their eigenvalues are localized to the unit interval. A generalized contractive behavior is described for the solutions of Riccati differential equations; it defines an equivalent condition between these equations and the dynamical systems