Static feedback design in linear discrete-time control systems based on training examples

The problem of static feedback design in linear discrete time-invariant control systems is considered. The desired behavior of the system is defined by a set of its output variation laws (training examples) and by a requirement to the degree of its stability. Controller's structural constraints are taken into account. Explicit relations are obtained and an iterative method based on these relations is proposed to find a good initial approximation of the desired gain matrix and to refine it sequentially. In the general case, simple-structure gain matrices are found: in such matrices, only those components are nonzero that are necessary and sufficient to give the system the desired properties. Some examples are provided to illustrate the method.