Fikar, M.: Control of Multivariable Systems. Parametrization of all Stabilizing controllers. PhD thesis, Dep. of Process Control CHTF STU, 1994.

The dissertation titled ``Control of Multivariable Systems. Parametrization of all Stabilizing Controllers'' presents a study of two step control design based on algebraic theory of polynomial matrices.

In the first step, the basic minimum degree controller based on pole placement design is derived. The controller consists of feedback part, feedforward part and has integration properties. In the second step, generalized controller from the family of all stabilizing controllers is searched. Thus, the two step design enables to define further requirements on the overall system while preserving the former properties of basic controller. The derivation of the generalized controller is shown on two control problems.

Predictive generalized controller is designed according to predictive control approach and has similar properties as widely used model-based predictive controllers (GPC, DMC, \ldots). However, the main advantage lies in its stability properties prescribed by the designer. Moreover, it is possible to incorporate constraints. The resulting generalized controller has linear structure with time-varying coefficients.

Decoupling generalized controller is derived and conditions for its existence are given. The solution is obtained by rewriting of the polynomial equations to the set of linear equations. The control design is very simple and transfer function shaping criterion is applied.

Generalized predictive controller is implemented in the study of the chemical reactor control. The reactor is described by the set of differential and algebraic equations and modelled as the multivariable system with 2 inputs and 2 outputs. As the reactor is nonlinear, parameter estimation algorithm together with predictive controller is used. The simulations confirm the superiority of the controller compared to one-step design.