Observer design for Lipschitz systems with discrete-time measurements

Abstract

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.

Continuous-Discrete Observers for Time-Varying Nonlinear Systems: A Tutorial on Recent Results

“…The robustness of observers under discretization was studied in [5], and [1,10,15] used output predictors to design observers; see also the works [4,8,13,17,19]. The paper [2] designed continuous-discrete observers for nonlinear continuous time systems, where the input of the system satisfies a persistent excitation condition, and [18] covers systems that are linear in the state and have known inputs.…”

“…The search for more effective designs for observers for nonlinear systems has led to a substantial and complex literature [3,4,5,9,15,20,21]. The work is motivated by a plethora of real world applications where it may be difficult or impossible to measure the state variables.…”

“…The works [4] and [9] used this two step approach to show that when no measurement occurs, the estimation error is a solution of an appropriate unknown linear parameter varying system. This led to a construction of a framer, meaning, an upper and lower bound for the solution vector, in a vector sense, which made it possible to design correction terms that ensure that the estimation error asymptotically converges to zero.…”

“…In the recent work [16], we built on [4], by finding a new class of continuous-discrete observers for continuous time Lipschitz systems with discrete measurements. As in [4] and [8], the continuous-discrete observers in [16] are obtained in two steps.…”

“…As in [4] and [8], the continuous-discrete observers in [16] are obtained in two steps. First, when the output is not available for measurement, the state estimate is computed by integrating the model.…”