Abstract
Linear matrix inequalities (LMIs) describe algebraic conditions for various important properties of finite-dimensional linear systems. In this paper, we propose a unified synthesis method of controllers that satisfy LMI-conditions belonging to a certain class, which we define focusing on a structure shared by many LMIs in control theory. The class includes LMIs for some root-clustering conditions, the H∞ norm conditions and the H2 norm conditions for both continuous-time systems and discrete-time systems, and arbitrary combinations of these LMIs. The method reduces a synthesis problem to a convex optimization problem to solve a certain LMI on a finite-dimensional parameter space. A controller that solves the synthesis problem is always full-order, and we also parametrize the set of such full-order controllers with a convex parameter set. When the state of the plant is available, there exist static state feedback solutions if the problem is solvable.
