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We establish in this dissertation some simplified conditions
for the closed-loop stability of the linear multivariable unity-
feedback system and for the system to remain stable under
sensor or actuator failures. We also propose the
parametrizations of all stabilizing controllers and the
descriptions of all achievable I/O maps. Such controller
parametrizations and I/O map descriptions are applied to
characterize the set of all decoupling controllers, and lead to
simple computational algorithms for the construction
ofdecoupling controller, stable decoupling controller, and
decoupling controllers that retain the closed-loop stability
under sensor failures. By the algebraic property of our
analysis, most results in this dissertation can apply to
continuous-time systems as well as discrete-time systems. Based
on our characterization of decoupling controllers and the
corresponding computational algorithm, we develop an
optimization-based decoupling control design procedure which
can also apply to SISO system design without any
modifications. This design procedure is systematic in that the
design is improved in each iteration based on a well-defined
performance index. It is also practical in that many
engineering-level design specifications such as rise time,
maximum overshoot, plant input limit, and robust stability can
be easily incorporated into the optimization program. By our
formulation, there is no equality constraints which are in
general hard to achieve in optimization problems. This design
procedure has been implemented as an interactive CAD package
for use under MATLAB. Two illustrative design examples are
also proposed to verify the effectiveness of this design
approach.
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