Observer design for Lipschitz systems with discrete-time measurements

In this paper, the authors investigate the problem of designing an observer for Lipschitz nonlinear systems with discrete time measurements (continuous-discrete time systems). The result is based on reachability analysis to synthesize an upper approximation of a reachable set. When this approximation is given in terms of a convex combination of linear mappings, a sufficient condition is given in terms of linear matrix inequality which can be solved using LMI techniques. This approach seems to provide an efficient new tool to address the problem of observer design for a class of Lipschitz systems. An academic example is given to illustrates this point.

I. Introduction

The problem under consideration in this paper is a state estimation problem for a class of Lipschitz continuous time systems with discrete time measurements. The use of continuous-discrete observers to estimate the state of Lipschitz nonlinear systems has already been investigated in the literature. It can be traced back to Jazwinski who introduced the continuous-discrete Kalman filter to solve a filtering problem for stochastic continuous-discrete time systems (see [5]). Inspired by this approach, the popular high-gain observer introduced in [4] has been adapted to the continuous-discrete context in [3]. In this work, the algorithm updates the estimate in two different ways: i) when no measurement is available, the estimate is obtained by integrating the model. ii) when a measurement occurs, the observer makes an impulsive correction of the estimate.