Nonlinear control synthesis by sum of squares optimization: a Lyapunov-based approach

This paper addresses the state feedback control synthesis problems for nonlinear systems, either without or with guaranteed cost or H/sub /spl infin// performance objectives. By representing the open-loop nonlinear systems in a state dependent linear-like form and considering a special class of Lyapunov functions, sufficient conditions for the solutions to the above problems can be formulated in terms of state dependent linear matrix inequalities. Semidefinite programming relaxations based on the sum of squares decomposition are then used to efficiently solve such inequalities.