Observer synthesis under time-varying sampling for Lipschitz nonlinear systems

Abstract

In this work, the problem of observation of continuous-time nonlinear Lipschitz systems under time-varying discrete measurements is considered. This class of systems naturally occurs when continuous processes are observed through digital sensors and information is sent via a network to a computer for state estimation. Since the network introduces variations in the sampling time, the observer must be designed so to take them into account. Here impulsive observers, which make instantaneous correction when information is received, are investigated. Moreover, we consider time-varying observer gains adapting to the varying sampling interval. In order to deal with both continuous-time and discrete-time dynamics, a new hybrid model is used to state the problem and establish the convergence of the proposed observer. First, generic conditions are provided using a hybrid Lyapunov function. Then a restriction of the generic Lyapunov function is used to establish tractable conditions that allows the synthesis of an impulsive gain.

Observer design for continuous-time dynamical systems

“…Using the hybrid formalism proposed in [106], general conditions in the context of network communications have been proposed in [183] and [184] for robust nonlinear observers and reducedorder observers. More sophisticated designs have been developed for arbitrary constant sampling period [194,83], and more generally for sporadic measurements, using sample-and-hold strategies [195,3] or discrete updates of the estimate at the sampling times [166,98,92,212,53,150,5], among others.…”

Observer Design for Linear Aperiodic Sampled-Data Systems: A Hybrid Systems Approach

“…Such strategies essentially belong to two main families. The first one pertains to observers whose state is entirely reset whenever a new measurement is available and that run in open-loop in between such events [1], [3], [4], [16], [19], i.e., continuousdiscrete observers:…”

“…where F is a gain to be designed, which can be potentially selected to be dependent on the time elapsed in between measurements; see [1], [3], [19]. The working principle of the above observer is as follows, when no plant measurement is available, the observer behaves as a copy of the plant.…”

Observer analysis and synthesis for perturbed Lipschitz systems under noisy time-varying measurements

“…The works [5,11] use the approximation of reachable sets based on convex embeddings. Impulsive models and time-varying Lyapunov functions have been used in [6,3,16]. A classical issue when considering observer design is the problem of "robustness", i.e.…”