Resilient control design for polynomial nonlinear systems with controller gain variations

In this paper, we consider the resilient (non-fragile) controller design problem for polynomial nonlinear systems. The designed state feedback controller is capable of tolerating some level of controller gain variations. Based on the Lyapunov stability theorem and S-procedure, the synthesis condition will be formulated in polynomial but bilinear form of Lyapunov function and the controller gain jointly. An iterative scheme will be proposed to separate the joint search of two variables and convert the bilinear condition to linear form. Sum-of-Squares (SOS) programming will be utilized to obtain the tractable solution and gradually augment the Lyapunov function and the nonlinear control law to higher order polynomial forms so that the robust margin of control gain is optimized. An examples will be used to materialize the design scheme and demonstrate the improved robust stability margin against the controller gain variations.