A trace bound for a general square matrix product

Estimates of bounds on the solutions of Lyapunov and Riccati equations are important for analysis and synthesis of linear systems. In this paper, we propose new trace bounds for the product of two general matrices. The key point for removing the restriction of symmetry is to replace eigenvalues partly by singular values in the equation of bounds. The results obtained are valid for both symmetric and nonsymmetric cases and give tighter bounds in certain cases.