On the synthesis of output feedback controllers for increasing the domain of attraction of piecewise polynomial systems

This paper addresses the computation of static nonlinear output feedback controllers for increasing the domain of attraction of an equilibrium point of piecewise nonlinear polynomial systems. Specifically, we consider continuous-time dynamical systems where the state space is partitioned into possibly overlapping regions, and where the vector field is defined independently among the regions by polynomial functions. We address the computation of static nonlinear output feedback controllers that increase the estimate of the domain of attraction provided by a polynomial Lyapunov function. The controller can be common or vary among the regions that partition the state space. A strategy based on sum-of-squares (SOS) programming is proposed, which provides guaranteed estimates of the increased domain of attraction and the controllers required to achieve them. Moreover, this strategy can be readily exploited with variable Lyapunov functions through the use of iterative algorithms. Two examples are given to illustrate the proposed strategy.