Hamiltonian Matrices and Algebraic Riccati equations

The main subject of this book is matrix Riccati differential equations; by definition, in this book, these are differential equations which can be written in the form $$ \dot W = M_{21} (t) + M_{22} (t)W - WM_{11} (t) - WM_{12} (t)W,t \in \mathcal{I}, $$ (RDE) with W, M 21(t) ∈ ℂmxn, M 22(t) ∈ ℂmxm, M 11(t) ∈ ℂnxn, M 12(t) ∈ ℂnxm for t ∈ \( \mathcal{I} \). Throughout Chapters 2-6 we agree for convenience that all coefficients of matrix Riccati equations are piecewise continuous and locally bounded and that \( \mathcal{I} \) is a non-degenerate interval on the real axis (or maybe an open subset of ℂ). We note that most of our results remain (a.e.) valid if the coefficients are locally integrable and if we understand the solutions in the sense of Caratheodory.