The strict bounded real lemma for linear time-varying systems

In this paper, we present a strict bounded real lemma for Linear time-varying systems in the infinite-horizon case. Using some operator methods, we show that the strict bounded realness for the related I/O operators is equivalent to the solvability of a semidefinite or definite Riccati equation. We also apply this result to the problem of disturbance attenuation and H-x-optimization. All our results include current ones in the literature for linear time-invariant systems. (C) 2000 Academic Press.