一类非线性切换系统观测器设计的新方法

A new approach to observer design for a class of switched nonlinear systems

针对一类切换规则为时间依赖型的Lipschitz非线性切换系统,采用驻留时间方法研究了状态观测器设计问题。该切换系统同时含有可观测子系统与不可观测子系统,通过构造合适的Lyapunov函数,并利用矩阵不等式技术得到了保证状态观测器状态估计误差收敛的条件。并给出了观测器设计步骤。进一步,通过矩阵变换将观测器增益求解转化为LMI形式。最后给出了仿真算例说明了该设计方法的有效性。

To design state observer for the switched systems with Lipschitz nonlinearity and time-dependent switching law, the dwell time approach is adopted. The switched system under consideration is composed of both observable and unobservable subsystems. By constructing appropriate Lyapunov functions and using ma- trix inequality techniques, some conditions of the convergence of the estimated state error for the state observer are obtained, and the design procedure of the observer is presented. Furthermore, by matrix transformation techniques, the solution to the corresponding observer gain is formulated in the form of a set of linear matrix in- equalities（LMIs）. Finally, a simulation example is given to demonstrate the effectiveness of the proposed approach.