Stabilization of Time-Varying Nonlinear Systems With Distributed Input Delay by Feedback of Plant's State

Abstract

International audienceWe address the problem of stabilizing systems belonging to a family of time-varying nonlinear systems with distributed input delay through state feedbacks without retarded term. The approach we adopt is based on a new technique that is inspired by the reduction model technique. The control laws we obtain are nonlinear and time-varying. They globally uniformly exponentially stabilize the origin of the considered system. We illustrate the construction with a networked control system

Global stabilisation of a class of feedforward systems with distributed delays

“…→ R is the so-called delay kernel, which is assumed to be a measurable function (see [12,16]), d ≥ 0 is a known constant delay (see [14,18]) and μ i , λ i , i = 1, 2, . .…”

“…Then, as the stability analysis conducted in [3], we can know that (18) and (19) is the output feedback controller of system (8).…”

Predictor-feedback stabilization of multi-input nonlinear systems

“…a) Background and Motivation: Despite the recent outburst in the development of predictor-based control laws for nonlinear systems with input delays [5], [6], [7], [8], [9], [10], [11], [13], [14], [15], [16], [17], [26], [27], [28], [29], [30], [31], [32], [35], [36], [37], [42], [43], [44], [45], [46], the problem of the systematic predictor-feedback stabilization of multi-input nonlinear systems with, potentially different, in each individual input channel, long input delays, has remained, heretofore, untackled, although the problem was solved in the linear case in the early 1980s [4] (see also [41]). In this article, we address the problem of stabilization of multi-input nonlinear systems with distinct input delays of arbitrary length and develop a nonlinear version of the prediction-based control laws developed in [4] and recently in [53], [54] for the compensation of input delays in multi-input linear systems.…”

Simultaneous compensation of input and state delays for nonlinear systems

“…Numerous results also exist on the control and analysis of nonlinear systems with input delays [16][17][18][19][20][21][22][23][24][25][26][27]. Few results exist on the compensation of input delay for systems with simultaneous delay on the state, even for linear systems [28][29][30].…”