H∞-differential Riccati equations: convergence properties and finite escape phenomena

The paper studies the transient and asymptotic behavior of the solution of the sign-indefinite differential Riccati equation (DRE) arising in finite-horizon H_∞-filtering and control problems. Differently from the sign-definite H_∞-DRE, the solution of the H_∞-DRE can have finite escape times even for nonnegative initial conditions. Sufficient and necessary conditions for boundedness and convergence are derived in correspondence to a fixed value of the H_∞-norm attenuation level γ. Finally, a stepwise γ-switching strategy is devised to guarantee boundedness as well as asymptotic performance