TWO THEOREMS ON THE DETERMINATION OF WEIGHTING MATRICES

Give a Linear time invariant discrete-time or continuous-time system and a corresponding quadratic cost function,relations are to be determined among the open-loop and the closed-loop characteristic polynomials,the coefficient matrices of the control system and the weighting matrices in the cost function.As a result,the determination of the weighting matrices only requires to solve a set of nonlinear equation sets with quadratic variables,which can be solved without much difficulty.