Design of linear systems with a quadratic criterion and structural constraints

The paper is concerned with a uniform approach to the problem of design for linear systems with a quadratic criterion and structural constraints on the feedback matrix (FM). The conditions for the minimum of the performance criterion are expressed in terms of some critical functions of FM elements. In the presence of arbitrary constraints on the FM this makes it possible to reduce the design problem to conditional minimization of the function of many variables. Conditions are found for existence of a control law optimal, in the sense of the minimal criterial function of the control law. A comparison is made with the well-known results in the field of linear system design in the case of constraints.