Robust Control for Two-Time-Scale Discrete
BALASAHEB M. PATRE
SGGS Institute of Engineering and Technology, Vishnupuri, Nanded–431606, India,
e-mail: firstname.lastname@example.org, email@example.com
Systems and Control Engineering, Indian Institute of Technology, Bombay, Mumbai–400 076, India,
(Received: 23 February 2003; accepted: 5 April 2005)
Abstract. Theproblem of designing robust controller for discrete two-time-scale interval systems,
conveniently represented using interval matrix notion, is considered. The original full order two-
time-scale interval system is decomposed into slow and fast subsystems using interval arithmetic.
The controllers designed independently to stabilize these two subsystems are combined to get a
composite controller which also stabilizes the original full order two-time-scale interval system. It is
shown that a state and output feedback control law designed to stabilize the slow interval subsystem
stabilizes the original full order system provided the fast interval subsystem is asymptotically stable.
Theproposed design procedure is illustrated using numerical examples for establishing the efﬁcacy
of the proposed method.
Theinterval systems are those whose parameters are known to lie within a range
rather than having an exact value. They are said to have parametric uncertainty.
Various analysis and design techniques available for such systems are essentially
meant for application to a “nominal” model. The resulting design is said to be
robust if the system performs within acceptable limits in the face of signiﬁcant
parameter variations and model uncertainties. The need to incorporate robustness
in design is necessitated by the fact that for most practical systems, the model is
known only approximately. For example, in the aircraft industry, the aircraft model
is constructed using the data obtained from the wind-tunnel experiments on the
aircraft body. As a consequence, the parameters of the model would not have a
speciﬁc value, rather they are known to lie within an interval. Since the actual ﬂight
data are not available the controller should be able to account for the unmodeled
parameters that can be obtained only when the aircraft is airborne. The other
examples include robotic manipulators, nuclear reactors, electrical machines and