H-INFINITY-DIFFERENTIAL RICCATI-EQUATIONS - CONVERGENCE PROPERTIES AND FINITE ESCAPE PHENOMENA

The paper studies the transient and asymptotic behavior of the solutio n of the sign-indefinite differential Riccati equation (DRE) arising i n finite-horizon H-infinity-filtering and control problems. Differentl y from the sign-definite H-2-DRE, the solution of the H-infinity-DRE c an have finite escape times even for nonnegative initial conditions. S ufficient and necessary conditions for boundedness and convergence are derived in correspondence to a fixed value of the H-infinity-norm att enuation level gamma. Finally, a stepwise gamma-switching strategy is devised to guarantee boundedness as well as asymptotic performance.