X. WEI ET AL.
Disturbance observer was established in the late of 1980s for linear frequency-domain systems,
has a simple structure and is easily implemented in engineering [6]. The motivation is suggested by
the fact that if the disturbances can be estimated, then the control of the uncertain dynamic systems
with disturbances may become easier [7]. In the past few years, disturbance-observer-based control
(DOBC) strategies were successfully used in achieving robust stability and performance in motion
control systems, for instance, robot manipulators [8], CNC machine centers in cutting process
[9], high-speed direct-drive positioning table [10], permanent magnet synchronous motor [11],
magnetic hard drive servo system [12] etc. Reference [13] gives a unified and historical review of
disturbance observer design for the benefit of practitioners. It appears that disturbance observers
mentioned above are mostly designed for linear systems. Recently, DOBC has been extended from
linear systems to nonlinear systems [14, 15]. In [14], single-input–single-output nonlinear systems
with well-defined disturbance relative degree were studied, and the disturbances were limited to be
constant or harmonic signals. In [15], the DOBC approaches for a class of multiple-input–multiple-
output (MIMO) nonlinear systems have been considered and the disturbances were represented by
a linear exogenous system. This extended the assumptions of the disturbances, which were limited
to be constant, harmonic in [16, 17]. However, it has been reported that when the disturbance has
perturbations, the proposed approaches in DOBC [14, 15] are unsatisfactory.
Sliding-mode control (SMC) is well known for their robustness to system parameter variations
and disturbances, which helps in achieving a satisfactory level of robustness and invariant behavior
by a simple method of changing the structure of the control according to the system states [18].
Based o n the robustness of SMC, a type of control scheme combining the DOBC with terminal
SMC is proposed for a class of MIMO continuous nonlinear systems in [19]. Besides continuous-
time SMC, research interest has developed for the area of discrete-time sliding-mode control
(DSMC) in the recent years [20–22]. The invariance property presented in continuous time sliding
mode is not preserved in discrete-time sliding m ode. Here, the system states move about the sliding
manifold are unable to stay on it; hence, giving the terminology quasi-sliding mode (QSM) [23].
Few researchers have also attempted the design of SMC of discrete-time systems with unmatched
uncertainties [24].
The disturbances concerning above are m ostly from single source, so can be estimated and
attenuated by a single controller. However, multi-source disturbances widely exist in circuits and
systems, telecommunications, signal processing, the control community, etc. Usually these distur-
bances are classified into two categories based on the error and noise analysis of future knowledge.
One are often assumed to generated by an exogenous system with uncertainty, which can represent
the disturbances with partial known information. The other is supposed to be the bounded H
2
norm
or random model, which can represent the disturbances with unknown information. The two type
of controller can be designed for the two type of disturbances model, then integrated as a composite
controller. However, the coupling from different disturbance controller can cause complex structure
of closed-loop system [25]. The stability and the disturbance attenuation performance guaranteed
by single controller cannot be guaranteed by the composite controller.
Considering most of the aforementioned research results about DOBC is concerned with contin-
uous systems, in this paper, a novel type of composite stratified anti-disturbance control scheme
is proposed for a class of MIMO discrete-time systems with multi-source disturbance, which
improves the defect of only traditional control method in terms o f the disturbance attenuation and
rejection. In the following, for a vector v(k), its Euclidean norm is denoted as v(k)=
v
T
(k)v(k)
and its L
2
norm is denoted as v(k)
2
=
∞
k=1
v(k)
2
.
2. FORMULATION OF THE PROBLEM
The following MIMO discrete-time system with nonlinear dynamics and two types of disturbances
is considered
x(k +1)= G
0
x(k)+ F
01
f
01
(x(k),k)+ H
0
[u(k)+d
0
(k)]+ H
1
d
1
(k)(1)
Copyright 䉷 2011 John Wiley & Sons, Ltd.
DOI: 10.1002/rnc
454
Int. J. Robust. Nonlinear Control
2012; :
–
22 453 472