广义线性离散系统的基于状态补偿的全维状态观测器的设计

The design of normal observer of full-dimensionality for linear discrete generalized systems based on state compensating

主要讨论了广义离散线性系统Ex(k+1)=Gx(k)+Hu(k)y(k)=Cx(k)+Du(k)的状态观测器,利用矩阵的奇异值分解和矩阵的广义逆,将广义线性系统化为奇异值标准形∑x1(k+1)=G11x1(k)+G12x2(k)+H1u(k)0=G21x1(k)+G22x2(k)+H2u(k)y(k)=C1x1(k)+C2x2(k)+Du(k)再引入状态补偿反馈u(k)=K1x2(k)+v(k),使得广义系统变为正常系统,从而设计出广义离散线性系统的全维状态观测器。x(k+1)=(G-KC)Vx(k)+(H-KD)u(k)u(k+1)+Ky(k)

For the following linear discrete generalized systems Ex(k+1)=Gx(k)+Hu(k),y(k)=Cx(k)+Du(k)(E∈Rn×mrank E<min{n,m}), the normal observer of fulldimensionality for this system is discussed. Using singular values decomposition of matrix and generalized inverse of matrix, the singular values standard form for this system is studied. The generalized systems based on state compensating are changed normal systems. That the design of normal observer of full-dimensionality for linear discrete generalized systems is given the following formula:(k+1)=(-K)V(k)+(-K)u(k)u(k+1)+Ky(k) .