Kronecker product and singular value decomposition of weighted extended matrix;

In this paper,based on the ordinary singular value decomposition,a quantitative correspondence of the singular values and singular vectors between the row or column symmetric matrix (namely,the extended matrix) and its original (a k a mother matrix) is derived,and the perturbation analysis for the extended matrix is provided accordingly.

When the extended matrix Rk(A) is not equal to its perturbation matrix R~k(A),the perturbation bounds under additvie perburtation and multiplicatvie perturbation are deducted,by means of singualr value decomposition,the decomposited subunitary facotrs of the extended matrix Rk(A),and its perturbation matrix R~k(A) in generalized polar decomposition under Frobenius norms.

By this ,this paper provide three training methods using weight matrix to emphasize the inherent differen.

It is the key technology for design of the constant beamwidth array to calculate the weight matrix.

A direct method to detecmine based on simple explicit relation among the optimal state feedback matix and the weighting matrices is proposed This method don′t need to do recursive calculation or complex transform for solving It is an effective approach to elminate the ″bottleneck″ problem that are caused by the application of LQ optimal theory to the engineerin

MPC solved a constrained convex quadratic optimization by defining reference trajectories, constraint limits, prediction horizon, control horizon and weighting matrices.

Based on the Hamiltonian system\'s theory,the relationship between closed-loop poles of system characteristic equation and weighting matrices was thoroughly investigated.