一类控制机构特性不确定非线性系统的镇定

Stabilization of a class of nonlinear systems with uncertain controllers' characteristics

运用非线性系统的精确线性化方法和Ｌｉｅ代数工具，将一类满足一定条件的，其中一个输入控制机构特性不确定的双输入－单输出仿射型非线性系统变换成直接型的普里叶系统，再应用鲁里叶的绝对稳定性判据，通过选择恰当的状态反馈矩阵，使所得直接型鲁里叶闭环系统绝对稳定于坐标原点，从而使得原非线性系统在给定的控制机构不确定特性范围内镇定于其平衡点，并且求得了镇定控制律的解析形式。本文在将鲁里叶理论推广到非线性情形的同时，解决了一类不确定系统的镇定问题。一个设计例子及仿真结果验证了本文提出方法的正确性。

Using the exact linearization method of nonlinear systems and tool of Lie algebra,a class of two inputs-single output affine nonlinear systems with uncertain controller'scharacteristic of one input are transformed into the direct Lurie's systems. The directLurie 's systems are stabilized at the origin point through Lurie's criterion of absolute stabilityand appropriate selection of state feedback matrix. Therefore, the original nonlinear systemsare stabilized at their equilibria under the given domain of uncertainty, and the analytic control laws are thus obtained. We augment the Lurie's theory, at the same time the stabilizationproblem of the original uncertain systems is solved. The correctness of the design method presented in this paper is demonstrated by an example and its simulation results.