Cascade High Gain Predictors for a Class of Nonlinear Systems

Abstract

International audienceThis work presents a set of cascade high gain predictors to reconstruct the vector state of triangular nonlinear systems with delayed output. By using a Lyapunov-Krasvoskii approach, simple sufficient conditions ensuring the exponential convergence of the observation error towards zero are given. All predictors used in the cascade have the same structure. This feature will greatly improve the easiness of their implementation. This result is illustrated by some simulations

High-gain-predictor-based output feedback control for time-delay nonlinear systems

“…[6][7][8]. In [9], the authors extended the result in [5] to a time-varying delay system and for only one observer; meanwhile, they concluded that the maximum bound of the delay should be sufficiently small. Former researches devoted to proving the exponential convergence of observer estimation errors.…”

Fixed-time observer with simple gains for uncertain systems

“…A second one, based on the Lyapunov auxiliary theorem and a direct change of coordinates, can be found in [2]. A third strategy for the class of uniformly observable systems use high-gain observers [18,15,1]. Other methods usually rely on a specic structure such as backstepping, adaptive observers, H ∞ observer, etc.…”

Dynamic observation-prediction for LTI systems with a time-varying delay in the input

“…The advantage is that no discretization is required to compute the prediction. The idea has also been used for the observation of systems with delayed output [15], [16], [17]. Recently, some works have used the same idea of dynamic prediction for control purposes: [18] with full state knowledge, [19] and [20] considering sample and hold phenomena.…”