On Lower Bounds of the Solution of the Discrete Time Algebraic Riccati Equation

In this paper, the estimation problem of solution of the general discrete time algebraic Riccati equation (GDTARE) is discussed. First, the equivalent of the GDTARE is given by using the formula of matrix inversion; then, three new lower bounds for the trace of the solution of the GDTARE are derived by means of the properties of eigenvaules and traces of matrices; Compared to the majority of the approach proposed in the literature, the present results have less conservative under certain conditions and the illustration is made with two numerical examples.