Stabilizing dynamic feedback design of quasi-polynomial systems using their underlying reduced linear dynamics

Based on the underlying dynamically similar linear system of a quasi-polynomial (QP) system [7], a dynamic feedback controller for single input QP systems is proposed in this work that can locally stabilize the closed-loop system using a pre-defined quadratic control Lyapunov function. Since the parameter matrix of the dynamically similar reduced linear dynamics depends linearly on the feedback gain parameters, the controller can be designed by solving LMIs. Conditions for extending the controller design for obtaining a globally stable closed-loop system are also investigated.