Feedback design for pendulum-like systems guaranteeing gradient-like behavior

This work concerns the problem of feedback design for pendulum-like systems guaranteeing gradient-like behavior. The uncertain system under consideration is described by a state-space model, which contains parameter uncertainties in both the state and input matrices. The nonlinearity is assumed to be periodic and slope restricted. First, the frequency-domain inequalities condition of gradient-like behavior is converted into a linear matrix inequalities (LMI) based criterion. Then the result is extended to take into account the parameter norm-bounded uncertainties in the linear part and derive static state feedback controller and dynamic output feedback controller such that the resulting closed-loop system is gradient-like. Schemes of designing controller as well as parameterized form of controllers are presented. Illustrative example is given to show the effectiveness of the proposed approach.