一种显式构造非奇异对象降阶H∞控制器的算法

目前显式构造降阶H_∞控制器的算法仅适用于奇异H_∞控制情形,为对非奇异情形使用这些算法,将广义对象的矩阵 A 分为 A ₀和 Δ A 2部分,并且使( A ₀, B ₁, C ₂, D ₂₁)或 ( A ₀, B ₂, C ₁, D ₁₂)含有不稳定零点,从而可以使用构造降阶控制器的算法得到可用于构造降阶控制器的解( X , Y ).矩阵 A 的这种改变将使得对象的3个线性矩阵不等式中的1个发生改变,因此该解( X , Y )必须在 A 未改变时,代入发生改变的那个不等式并判断其是否成立,若成立则该解( X , Y )可用于对广义对象构造降阶控制器.数值算例表明了该算法的有效性.

Algorithm of constructing reduced-order H∞ controller for nonsingular plants in explicit form

Algorithms of constructing reduced-order H_∞ controllers in explicit form are only applied to singular H_∞ control case. In order to apply these algorithms to nonsingular case, the matrix A of a generalized plant was divided into two parts A ₀ and Δ A , then ( A ₀, B ₂, C ₁, D ₁₂) or ( A ₀, B ₁, C ₂, D ₂₁) had unstable invariant zeros. Those algorithms could be used to the changed system to get a solution ( X , Y ) that could be used to construct a reduced-order controller. Since one of three linear matrix inequalities of the initial generalized plant was changed by the change of the system matrix A , the solution ( X , Y ) must be used in the linear matrix inequality that was changed with the variation of A for the initial generalized plant to see whether it could still hold or not. If it was holden, the solution ( X , Y ) could be used to construct a reduced-order controller for the initial generalized plant. Effectiveness of the algorithm was shown by numerical examples.