Nonlinear control of uncertain systems via semidefinite programming

The last few years witnessed an increasing interest in the problem of control synthesis of nonlinear systems. A recently derived stability criterion for nonlinear systems which has a remarkable convexity property and the development of numerical methods for verification of positivity allows the computation via semidefinite programming of stabilizing controllers for the case of systems with polynomial or rational vector fields. Using the theory of semialgebraic sets these computational tools are extended in this paper for the case of polynomial or rational systems with uncertain parameters