Abstract
This paper presents some comparison and uniqueness theorems for periodic Riccati differential equations (PRDEs). Precisely, it is first shown that for a PRDE with a positive semidefinite coefficient matrix in the quadratic term under the assumption of stabilizability, the solubility of the corresponding Riccati differential inequality implies that the PRDE admits a maximal solution. Furthermore, for the class of PRDEs 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 positive definite coefficient matrix in the constant term, it is concluded that the stabilizing solution (if any) is also unique and using this uniqueness result another uniqueness theorem of the stabilizing solution for the general PRDE is derived.
Published Version
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