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 ofP, the plant transfer function, andQ=H_{y₁u₁}. In particular, the I/O transfer functionQ=H_{y₂,u₁}=PQ. Using the framework of rational transfer functions, we show that the closed-loop system will be exponentially stable if and only ifQis exponentially stable. Furthermore, if bothPandQare 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.