H/sub /spl infin//-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/sub /spl infin//-filtering and control problems. Differently from the sign-definite H/sub /spl infin//-DRE, the solution of the H/sub /spl infin//-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/sub /spl infin//-norm attenuation level /spl gamma/. Finally, a stepwise /spl gamma/-switching strategy is devised to guarantee boundedness as well as asymptotic performance.