Designing a linear controller for polynomial systems with the largest domain of attraction via LMIs

The problem of designing a linear controller for nonlinear polynomial systems that results the largest domain of attraction is considered. Moreover, using the proposed algorithm, the shape of the approximation of domain of attraction can be defined, due to importance and change of different states of system. To compute the estimate of the region of attraction, a Lyapunov function has been used. The designing problem involves solving a double nonconvex optimization problem, which can be changed to a semiconvex optimization problem, via linear matrix inequalities (LMI).