Generalized Time-Varying Riccati Theory: A Popov Operator Based Approach

We derive in this paper necessary and sufficient conditions for theexistence of the stabilizing solution to the differential Riccati equation, withindefinite sign quadratic term. The key object of the present approach isthe Popov operator, associated with a controlled exponentially dichotomicevolution and a quadratic cost. Special attention is paid to the classical positivitytheory and a time-varying version of the celebrated Kalman-Yakubovich-Popov Lemma is given under relaxed assumptions.