Firstly the TPS is introduced into the theory of Semi-parametric regression,and then the regular matrix R is deduced.

Making use of Beasley s Lemma and permanent we obtain the row rank, column rank and Schein rank are identical for a regular matrix over a commutative semiring and the necessary and sufficient conditions for invertibility of matrices over an incline.

Robust lower guaranteed cost fault tolerant control for interval matrix systems;

The planar magnetic levitation system was a nonlinear uncertain system,the interval matrix minimum upper bound methods was proposed to design robust control.

Designed state feedback controller with gain is also interval matrix.

Further,by using the technique of matrix eigenvalues boundary,some simple and applicable algebraic criteria of the stability,the instability and the mixed stability for the interval matrices and discrete dynamic systems have been gained.

Considering that the network-induced delay is a constant,which is less than one sampling period,Lyapunov Function,linear matrix inequality(LMI) and interval matrices technique are used to design the local optimal controller gain for state feedback network control systems.

One of the crucial steps is choosing an appropriate regularizer in processing GPS systematic errors based on the semi-parametric model.

Two new regularizers are employed to separate systematical errors in GPS baselines.

On the one hand,the ill condition of the normal equation was weakened by proper selection of a reasonable regularizer based on TIKHONOV regularization principle and much precision float ambiguities were obtained.