不满足匹配条件的不确定离散系统的鲁棒控制

研究了一类不满足匹配条件的不确定离散系统的二次鲁棒镇定问题，系统的不确定部分为时变、范数有界。通过求解离散代数Riccati方程获得鲁棒镇定增益阵，同时，此Riccati方程的对称正定解也是建立闭环系统渐近稳定性的Lyapunov矩阵。所获得的结论与现有的结果相比，不需要引入增广系统或辅助系统，就可以解决同时含有状态矩阵和输入矩阵不确定性的离散系统的鲁棒镇定问题，本结果可以看成是以前获得的关于连续系统鲁棒镇定结果的离散系统对应。

Robust Control of Uncertain Discrete Systems Under Unmatched Conditions

In this paper, the problem of robust stabilization of a class of uncertain discretesystems under unmatched conditions in investigated. The uncertain part of the systems is time-varying and norm -bounded. The robust stabilizing gain matrix is obtained by solving adiscrete algebraic Riccati equation, simultaneously the positive definite symmetric solution ofthe Riccati equation is also the Lyapunov matrix which builds the asymptotic stability of theclosed - loop systems. Comparing with the available results, the robust stabilizing problemcan be solved without the extended or auxiliary Systeme when the perturbations enter into bothstate matrix and input matrix. the result can he seen as the correspondent ones obtained previously in the continuous- time systems.