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Delay-dependent Robust H∞ Control for Uncertain
Nonlinear System Based on Fuzzy Hyperbolic Model with
5
10
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20
25
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35
40
Time-Varying Delays#
Wang Gang*
(School of Information Science and Engineering, Northeastern University, ShenYang 110819)
Abstract: The robust H∞ control problem was considered for a class of fuzzy hyperbolic model with
time-varying delays (DFHM) systems with parametric uncertainties. First, DFHM modeling method
was presented for time-delay nonlinear systems. Then, by using Lyapunov-Krasovskii approaches,
delay-dependent sufficient condition for the existence of a kind of state feedback controller was
proposed, which was expressed as linear matrix inequalities (LMIs). The controller can guarantee that
the resulting closed-loop system is robustly asymptotically stable with a prescribed H∞ performance
level for all admissible uncertainties and time-delay. Finally, a simulation example was provided to
illustrate the effectiveness of the proposed approach.
Keywords: asymptotically stable; fuzzy hyperbolic model with time-varying delays; robust H∞ control;
parameter uncertainties
0 Introduction
In the past decades, fuzzy logic control has become an effective approach to control
complex and ill-defined systems for which the application of conventional control techniques is
not straightforward or feasible. It has been proven that fuzzy logic control is an effective approach
when dealing with complex nonlinear systems [1], [4]-[8].
On the other hand, time delays are frequently encountered in various areas such as
engineering systems, biology and economics. The existence of time delays is often the main cause
of instability and poor performance of a control system. Moreover, when modeling real-time
plants, the parameter uncertainties are unavoidable, which would lead to perturbations of the
elements of a system matrix in a state-space model. Therefore, stability analysis and designing of
robust controllers for uncertain nonlinear systems with t
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