Truncated Prediction Output Feedback Control of a Class of Lipschitz Nonlinear Systems With Input Delay

Abstract

This brief addresses an output feedback control design for Lipschitz nonlinear systems in the presence of input delay. A nonlinear observer is introduced to estimate the system states. A truncated predictor state feedback, which is the conventional predictor state feedback law with the distributed term dropped, is implemented with the estimated states. Lyapunov-Krasovskii functionals are constructed to establish conditions under which this observer-based truncated predictor feedback law asymptotically stabilize the system at the origin. The effectiveness of the proposed method is demonstrated on the Chua's circuit.

Truncated Predictor Control of Lipschitz Nonlinear Systems With Time-Varying Input Delay

“…Our results in this paper generalize our recent work [26], where TPF design method was adopted to achieve output feedback stabilization in the presence of constant delay in the input. The difficulty arises from the stability analysis in the presence of time-varying delay.…”

“…There are also a few results on the stabilization of inputdelayed nonlinear systems by output feedback. Although there have been some results developed on the observer design for Lipschitz nonlinear systems [24], [25], [26], the observerbased control designs are non-trivial, due to the fact that the separation principle does not hold in general for nonlinear systems.…”

“…The difficulty arises from the stability analysis in the presence of time-varying delay. The extension of the result derived in [26] to the stabilization problem for Lipschitz nonlinear systems with time varying input delay is nontrivial. Moreover, the output feedback design in this paper only requires the knowledge of Lipschitz constant for the nonlinear function and thus is robust to the nonlinearity, which is significantly different from the design in [26].…”

Prediction‐Based Control for Nonlinear Systems with Input Delay

“…The works in [22][23][24] elaborate on the limitations of the finite spectrum assignment. Authors of [25] and [26] propose truncated output feedback controllers for linear systems and a class of Lipschitz nonlinear systems, respectively, to avoid implementation problems. Truncated output feedback controllers safely ignore the infinite dimensional term.…”

“…predictor (9) (with = 0) becomes the classical Luenberger observer for system (26). In this case, from (7), ( ) = ( ).…”