A weighted switching sequence optimization algorithm for static output feedback control synthesis of nonlinear systems

In this paper, the static output feedback (SOF) control synthesis of discrete-time Takagi-Sugeno (T-S) fuzzy systems is concerned upon homogeneous polynomial parameter dependent Lyapunov functions (HPPD-LFs). It is well known that SOF control always leads to inequality conditions with non-convexity, which makes the optimization problem intractable. To overcome this difficulty, a novel switching sequence convex optimization (SSCO) algorithm is proposed, which is upon the matrix decomposition concept and the inner approximation strategy to eliminate the non-convex terms formed by the controller and the slack variables. Unlike conventional methods, the controller acts as a direct optimization variable and does not require structural or multiplicative relationships between the slack variables, which opens up the possibility of obtaining improved results in terms of $l_2$ gain performance. In particular, more relaxed design conditions are obtained for SOF controller based on the weighted switching method by effectively utilizing the membership functions information. Finally, two simulation examples demonstrate the superiority of the developed SOF control scheme.