Matrix solution bounds of the continuous Lyapunov equation by using a bilinear transformation

Solution Bounds and Numerical Methods of the Unified Algebraic Lyapunov Equation

“…Combined with Theorem 1 and Theorem 2, we can give a lower matrix bound of the positive definite solution P of UALE (8). Theorem 3.…”

“…Next, we prove that the matrix sequence {P k } generated by (22) converges to the positive definite solution of UALE (8).…”

“…Theorem 7. Assume that the conditions given in the Theorem 6 are satisfied, the sequence {P k } generated by the iterative scheme (22) converges, and converges to the unique positive definite solution P + of UALE (8).…”

“…Zhang et al in [7] extended the upper and lower bound of the solution of UALE on δ-domain. Besides, UALE can be transformed into a quasi-standard form of the DALE by using a bilinear transformation proposed in [8]. Thus, by extending this approach for CALE associated with linear algebraic techniques, Lee present several upper and lower matrix bounds of the solution of UALE in [9].…”