Regulation and robust stabilization: a behavioral approach

PhD ceremony: Mr. F. Shaik, 16.15 uur, Academiegebouw, Broerstraat 5, Groningen

Thesis: Regulation and robust stabilization: a behavioral approach

Promotor(s): prof. H.L. Trentelman

Faculty: Mathematics and Natural Sciences

In his thesis Fiaz Shaik considers a number of control synthesis problems within the behavioral approach to systems and control. In particular, he considered the problem of regulation, the H∞ control problem, and the robust stabilization problem.

He also studied the problems of regular implementability and stabilization with constraints on the input/output structure of the admissible controllers. The systems in Shaiks thesis are assumed to be open dynamical systems governed by linear constant coefficient ordinary differential equations. The behavior of such a system is the set of all solutions to the differential equations. Given a plant with its to-be-controlled variable and interconnection variable, control of the plant is nothing but restricting the behavior of the to-be-controlled plant variable to a desired subbehavior. This restriction is brought about by interconnecting the plant with a controller (that we design) through the plant interconnection variable. In the interconnected system the plant interconnection variable has to obey the laws of both the plant and the controller. The interconnected system is also called the controlled system, in which the controller is an embedded subsystem. The interconnection of the plant and the controller is said to be regular if the laws governing the interconnection variable are independent from the laws governing the plant. We call a specication regularly implementable if there exists a controller acting on the plant interconnection variable, such that, in the interconnected system, the behavior of the to-be-controlled variable coincides with the specication and the interconnection is regular.

Within the framework of regular interconnection Shaiks solves the control problems listed in the first paragraph of this summary. Solvability conditions for these problems are independent of the particular representations of the plant and the desired behavior.