基于输出反馈的多输入多输出系统同时稳定控制

On Simultaneous Stability of Linear MultiInput MultiOutput Systems via Output Feedback Controller

对多输入多输出系统，基于输出反馈，作者根据Ｈｕｒｗｉｔｚ稳定性理论，得到了一种多重系统同时稳定的充分必要条件，基于这一充分必要条件，通过引入二次型性能指标和非线性约束优化理论，得到了一种同时稳定的容错控制设计算法。

Paskota (1994) suggested a procedure to design faulttolerent controller; the controller designed by his procedure can simultaneously stabilize multiple systems, but Paskota only discussed singleinput system. How to deal with the problem of multiinput system′s simultaneous stability is not yet solved. We give an algorithm to solve this problem; the main ideas are: (1) By employing the Hurwitz stability theory, we get a necessary and sufficient condition for the simultaneous stability of multiinput systems. (2) Based on the abovementioned condition, through introducing a quadratic cost function and adding constraints to input signals, we convert the simultaneous stability controller′s design into a nonlinear optimization, then we obtain an algorithm to solve the optimization. (3) The simulation results of a numerical example show that the controller designed by this algorithm does keep multiple systems simultaneously stable; at the same time, the system′s dynamic and static performance are satisfactory.