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This paper addresses the problem of global output feedback stabilization for a class of inherently higher-order uncertain nonlinear systems subject to time-delay. By using the homogeneous domination approach, we construct a homogeneous output feedback controller with an adjustable scaling gain. With the aid of a homogeneous Lyapunov-Krasovskii functional, the scaling gain is adjusted to dominate the time-delay nonlinearities bounded by homogeneous growth conditions and render the closed-loop system globally asymptotically stable. In addition, we also show that the proposed approach is applicable for time-delay systems under nontriangular growth conditions.

This paper addresses the global stabilization problem for a class of uncertain systems with delay which is described by

It has been known that the problem of global output feedback stabilization for uncertain nonlinear systems is very challenging compared to the state feedback case. In the past decade, global stabilization by output feedback domination method has been proved to be achievable for a series of nonlinear systems. For the system of a five-spot pattern reservoir, a nonlinear reduced-order model is identified and an asymptotically stabilizing controller is proposed based on the circle criterion in [

However, the aforementioned results have not considered the time-delay effect which is actually very common in state, input, and output due to the time consumed in sensing, information transmitting, and controller computing. In the case when the nonlinearities contain time-delay, some interesting results have been obtained. For instance, in [

In the case when only output is available, the problem of output feedback stabilization is more challenging and fewer results have been achieved for nonlinear systems with time-delay. For a linear system with time-delay in the input, the problem of output feedback stabilization of was solved in [

In this paper, we aim to tackle the problem by using the output feedback domination approach. First, based on homogeneous domination approach [

In this section, we show that under a lower-triangular homogeneous growth condition, the nonlinear time-delay system (

Consider the following:

When

First, we construct a output feedback stabilizer for the following linear system

There exists a dynamic homogeneous output feedback controller based on observer:

It can be verified that the closed-loop system (

Consider system (

The output feedback controller is constructed by introducing a scaling gain into the output feedback controller obtained in Lemma

Consider the following

Under Assumption

The proof is very similar to that of Theorem

Consider the following inherently nonlinear time-delay system.

Consider

State trajectories of

Time history of

In this paper, we have studied the problem of global output feedback stabilization for a class of higher-order time-delay nonlinear systems under a homogeneous condition. First, homogeneous output feedback controllers have been constructed with adjustable scaling gains. Then, with the help of a homogeneous Lyapunov-Krasovskii functional, we’ve redesigned the homogeneous domination approach to tune the scaling gain for the overall stability of the closed-loop systems. The output feedback controllers proposed in this paper are memoryless and, therefore, can be easily implemented in practice.

This appendix collects the definition of homogeneous function and several useful lemmas.

For a set of coordinates

The dilation

A function

A vector field

If the trivial solution

Denote

Suppose

There is a constant

Let

This work was supported in part by National Natural Science Foundation of China (61374038, 61273119, 61174076), Natural Science Foundation of Jiangsu Province of China (BK2011253), and Research Fund for the Doctoral Program of Higher Education of China (20110092110021).