An algorithm for the quadratic stabilization of uncertain systems with structured uncertainty of the one-block type

The main result of this paper is a sufficient condition for the quadratic stabilizability of a class of uncertain systems containing structured uncertainty. The uncertain systems under consideration are referred to as uncertain systems of the one-block type. The main requirement for such uncertain systems is that the number of (unmatched) uncertain parameters is less than or equal to the number of control inputs. In the quadratic stabilization algorithm presented, the uncertainty structure is exploited by the introduction of scaling parameters. A key advantage of the algorithm presented in this paper is that it is based on the solution of a Lyapunov equation. Moreover, the solution to this Lyapunov equation is a linear function of the scaling parameters. This enables the quadratic stabilizability of the system to be tested by solving a Linear Matrix Inequality problem in which the number of unknown variables is equal to the number of uncertain parameters.