COMPARISON AND UNIQUENESS THEOREMS FOR PERIODIC RICCATI DIFFERENTIAL-EQUATIONS

This paper presents some comparison and uniqueness theorems for period ic Riccati differential equations (PRDEs). Precisely, it is first show n that for a PRDE with a positive semidefinite coefficient matrix in t he quadratic term under the assumption of stabilizability, the solubil ity of the corresponding Riccati differential inequality implies that the PRDE admits a maximal solution. Furthermore, for the class of PRDE s mentioned above a monotonicity property is given. It is also proven that each stabilizing solution (if any) for this class of PRDE is just the maximal solution and thus is unique. Finally, for a PRDE with a p ositive definite coefficient matrix in the constant term, it is conclu ded that the stabilizing solution (if any) is also unique and using th is uniqueness result another uniqueness theorem of the stabilizing sol ution for the general PRDE is derived.