Global output tracking by state feedback for high-order nonlinear systems with time-varying delays

Abstract

This paper focuses on the problem of global practical output tracking for a class of high-order non-linear systems with time-varying delays (via state feedback). Under mild growth conditions on the system nonlinearities involving time-varying delays, we construct a state feedback controller with an adjustable scaling gain. With the aid of a Lyapunov-Krasovskii functional, the scaling gain is adjusted to dominate the time-delay nonlinearities bounded by the growth conditions and make the tracking error arbitrarily small while all the states of the closed-loop system remain to be bounded. Finally, a simulation example is given to illustrate the effectiveness of the tracking controller.

Global Practical Output Tracking for a Class of Uncertain Inherently Time-Varying Delay Nonlinear Systems by Output Feedback

“…However, when d i (t) = 0, the global output tracking of system (1) by output feedback is a relatively new problem because of a time-varying delay entering system states makes the control design more difficult because the existence of a timevarying delay effect makes the common assumption on the high-order system nonlinearities infeasible and which conditions should be placed to the nonlinearities remains unanswered. Assumption 4 represents the condition of the reference signal, which can already be called the standard condition for solving the tracking problem of nonlinear systems (see [3][4][5][6][7][8]28,[32][33][34]).…”

“…In (33), V n (z) and S(z) are homogeneous of degree 2σ − τ and 2σ with respect to the dilation weight ∆, respectively. Therefore, it follows from Lemma 2 that there exist constants λ i > 0 and i > 0…”

“…However, these works only investigated the partially linearizable case of System (1). Researchers [32,33] investigated and solved the problem by using state-feedback control. Recently, we have published research results on the issue of output-feedback control where the time delay is constant [34].…”