Unified, improved matrix upper bound on the solution of the continuous coupled algebraic Riccati equation

We develop a broad framework that leads to a unified, improved matrix upper bound on the positive semidefinite solution of the continuous coupled algebraic Riccati equation (CCARE). Our approach was largely inspired by recent works of Lee and of Davies, Shi, and Wiltshire. Our main result tightens the needed upper bounds on relevant dominant eigenvalues. Besides, it applies to a larger number of situations since a key restriction here is weaker as compared to those in Davies et al. Numerical evidence is also provided to demonstrate the behavior of the new matrix upper bound.