Title:

Output sampling based sliding mode
control for discrete time systems

This thesis concerns the development of outputbased sliding mode control schemes for
discrete time, linear time invariant systems. Unlike most of the work given in the literature in
this area, the work is concemed with the development of static output feedback based
discrete time sliding mode control schemes for nonminimum phase, nonsquare systems
with arbitrary relative degree and which include unmatched uncertainties. The key concept of
extended outputs in discrete time will be introduced. It will be shown that by identifying a
minimal set of present and past outputs an augmented system can be obtained which
permits the design of a sliding manifold based upon output information only, which renders
the sliding manifold stable. Any transmission zeros of the augmented plant will also be
shown to be among the transmission zeros of the original plant. It will also be shown that if
the extended outputs chosen span the state zero directions of an invariant zero of the
system, then the invariant zero disappears from the augmented system. Linear matrix
inequalities are then used for sliding surface design. For nonminimum phase, nonsquare
systems with unmatched uncertainties, it will be shown that in some cases the extended
outputs can be chosen such that the effect of the disturbance on the sliding surface can be
nullified. If this is possible, a procedure to obtain a Lyapunov matrix, which simultaneously
satisfies a Riccati inequality and a structural constraint and which is used to formulate the
control law that satisfies the reachability condition has been given. For the general case,
where the sliding surface is a function of the disturbance, a control law will be chosen such
that the effect of the disturbance on the augmented outputs and the sliding manifold will be
minimized. Another key contribution of this work is the use of extended outputs for
reconfigurable control under sensor loss. The reconfigurable control methodology presented
in this work is in discrete time and is a static output feedback based control scheme, unlike
most of the reconfigurable control schemes given in the literature which require an estimator
and which are continuous time based schemes. Suitable examples, which include multiple
sensor failures and a benchmark problem taken from the literature which represents the
lateral dynamics of the F14 aircraft, have been chosen to show the effectiveness of the
proposed control design methodologies.

L
Abstract
T his thesis concerns the development of out putbased sliding mode control schemes for
discrete time, linear time invariant systems. Unlike most of the work given in the literature
in this area, the work is concerned with the development of static output feedback
based discrete time sliding mode control schemes for nonminimum phase, nonsquare
systems with arbitrary relative degree and which include unmatched uncertainties. The'
key concept of extended outputs in discrete time will be introduced. It will be shown
that by identifying a minimal set of present and past outputs an augmented system can
be obtained which permits the design of a sliding manifold based upon output information
only, which renders the sliding manifold stable. Any transmission zeros of the
augmented plant will also be sho,wn to be among the transmission zeros of the original
plant. It will also be shown that if the extended outputs chosen span the state zero
directions of an invariant zero of the system, then the invariant zero disappears from the
augment.ed system. Linear matrix inequalities are then used for sliding surface design.
For nonminimurn phase, nonsquare systems with unmatched uncertainties, it will be
shown that in some cases the extended outputs can be chosen such ,that the effect of
the disturbance on the sliding surface can be nullified. If this is possible, a procedure
to obtain a Lyapunov matrix, which simultaneously satisfies a Riccati inequality and a
structural constraint and which is used to formulate the control law t hat satisfies the
reachability condit ion has been given. For the general case, where the sliding surface
is a function of the disturbance, a control law will be chosen such that the effect of
the disturbance on the augmented outputs and the sliding manifold will be minimized.
Another key contribution of t his work is the use of extended outputs for reconfigurable
control under sensor loss. The reconfigura~le control methodology presented in this work
is in discrete time and is a static output feedback based control scheme, unlike most of
t he reconfigurable control schemes given in the literature which require an estimator and
which are continuous time based schemes. Suitable examples, which include multiple
sensor failures and a benchmark problem taken from the literature which represents the
lateral dynamics of the F14 aircraft have been chosen to show the effectiveness of the
proposed control design methodologies.
