Continuous Sampled-Data Observer Design for Nonlinear Systems With Time Delay Larger or Smaller Than the Sampling Period

This technical note addresses the problem of high gain observer design for a class of triangular nonlinear systems with sampled and delayed output measurements. The transmission delay may be larger or smaller than the sampling period. Firstly, a class of hybrid systems are introduced, and sufficient conditions are proposed to guarantee that the hybrid systems are globally and exponentially stable. Then, a continuous-discrete observer is designed for the nonlinear systems. Based on these sufficient conditions and a specially constructed Lyapunov-Krasovskii functional, it is shown that the observation errors globally and exponentially converge to the origin. Finally, an illustrative example is used to verify the validity of the proposed design methods.