具有未知输出函数的非线性时滞系统的输出反馈稳定

Output Feedback Stabilization of Nonlinear Time-Delay Systems with Unknown Output Function

针对一类非线性函数、积分器及输入中都包含时滞的非线性系统,在输出信息不确定的条件下,研究其全局输出反馈稳定问题。由于积分器中的时滞项会使得运算更加麻烦。为解决这个问题,首先引入不包含时滞的积分器,然后为变换后的系统的标称系统构造合适的Lyapunov函数和齐次状态观测器,基于增加幂次积分法和齐次占优法,设计一个输出反馈控制器,确保标称系统全局渐近稳定。最后,通过坐标变换引入增益L,构造依赖于L的齐次状态观测器,Lyapunov-Krasovskii泛函,设计输出反馈控制器,使非线性系统全局渐近稳定。

The global output feedback problem is studied for a class of nonlinear systems whose nonlinear functions,integrators and input all contain time delays under the condition of uncertain output information.Since the time delays terms in the integrators can make the operation more troublesome.To solve this problem,we first introduce an integrator without time delays,then construct suitable Lyapunov function and homogeneous state observer for the nominal system of the transformed system,and design an output feedback controller based on adding a power integrator technique and homogeneous domination approach to ensure the global asymptotic stability of the nominal system.Finally,the gain L is introduced through coordinate transformation,a homogeneous state observer dependent on L,Lyapunov-Krasovskii functional,and an output feedback controller are designed to make the nonlinear system asymptotically stable.