Abstract.
We derive in this paper necessary and sufficient conditions for the existence of the stabilizing solution to the differential Riccati equation, with indefinite sign quadratic term. The key object of the present approach is the Popov operator, associated with a controlled exponentially dichotomic evolution and a quadratic cost. Special attention is paid to the classical positivity theory and a time-varying version of the celebrated Kalman-Yakubovich- Popov Lemma is given under relaxed assumptions.
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Ionescu, V., Stefan, R. Generalized Time-Varying Riccati Theory: A Popov Operator Based Approach. Integr. equ. oper. theory 48, 159–212 (2004). https://doi.org/10.1007/s00020-001-1192-2
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DOI: https://doi.org/10.1007/s00020-001-1192-2