New lower solution bounds for the continuous algebraic Riccati equation

Abstract

Abstract. In this paper, by constructing the equivalent form of the continuous algebraic Riccati equation (CARE) and applying some matrix inequalities, a new lower bounds solution of the CARE is proposed. Finally, corresponding numerical examples are provided to illustrate the effectiveness of the results.

New upper bounds on the solution matrix to the continuous algebraic Riccati matrix equation

“…Especially eigenvalues [10,12,25,27,37], trace [23,24,35] and determinant [17] bounds are derived. However, among these bound types, matrix bounds which include in lower matrix bounds [5,6,15,19,26,39,40,41] and upper matrix bounds [4,8,9,19,20,22,26,39,43] are the most general and useful ones because other bounds that are dependent on the eigenvalue can be directly derived from matrix bounds via monotonicity.…”