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In this thesis, three main topics of stability problem for
discrete uncertain multiple time-delay systems are investigated;
i.e. the optimal D-stable control for discrete multiple time-
delay systems with parametric uncertainties, the robust Kalman
filter synthesis of uncertain multiple time-delay stochastic
systems and the discrete LQG (linear-quadratic Gaussian) optimal
control of uncertain multiple time-delay stochastic systems.
The problem of optimal D-stability for discrete multiple
time-delay systems with parametric uncertainties is considered
in the first part of the thesis (Chapter 2). By properly defining
new state variables, a discrete uncertain multiple time-delay
system can be transformed into another system with no delay.
Thus, the problem of optimization of discrete-time systems with
multiple time delays is reduced to a standard discrete linear
quadratic regulator problem. Based on the technique of D-pole
placement, a robust criterion of D-stability is derived to show
that the optimal control law not only minimizes the discrete
linear quadratic performance index but also meanwhile guarantees
that all poles of the closed-loop system remain inside the
specified disk D(α,r) in the presence of parametric
uncertainties.
The robust Kalman filter synthesis and discrete LQG optimal
control of uncertain multiple time-delay stochastic systems are
considered in Chapter 3 and Chapter 4, respectively. In these
two chapters, minimax theory and Bellman-Gronwall lemma are
employed, based on the upper norm-bounds of parametric
uncertainties and noise uncertainties, a robust criterion is
derived to guarantee the asymptotic stability of the uncertain
stochastic system. Finally, two examples are given to illustrate
our main results.
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