Design of multivariable feedback systems with stable plant

This paper considers, in a general algebraic framework, the design of a unity-feedback multivariable system with a stable plant. The method is based on a simple parameterization of the four closed-loop transfer functions in terms of
P
, the plant transfer function, and
Q=H_{y_{1}u_{1}}
. In particular, the I/O transfer function
Q=H_{y_{2},u_{1}}=PQ
. Using the framework of rational transfer functions, we show that the closed-loop system will be exponentially stable if and only if
Q
is exponentially stable. Furthermore, if both
P
and
Q
are strictly proper then the controller is also strictly proper. The basic result is Design Theorem 2. An algorithm is given for obtaining strictly proper controllers such that the resulting I/O map is decoupled, all its poles can be chosen by the designer, and the same holds for zeros except, of course, for the C
+
-zeros prescribed by the C
+
-zeros of the plant. A discussion is included to temper these results by the constraints imposed by noise and plant saturation.