Solvability of norm-type discrete algebraic Riccati equation

This paper proposes a norm-type discrete algebraic Riccati Equation, which is a generalized version of the well-known standard discrete algebraic Riccati Equation, and has additional norm terms. Under stabilizability and assumption that the additional terms are not too large, the existence of a positive semidefinite solution is guaranteed. Application to guaranteed cost control is given.