Gradient-like behavior analysis and synthesis of uncertain pendulum-like systems

This paper focuses on uncertain pendulum-like systems subjected to norm-bounded parameter uncertainty in the forward path and a vector-valued periodic nonlinearity in the feedback path, and addresses the robust gradient-like behavior analysis and synthesis problems for such systems. Sufficient conditions for robust gradient-like behavior are derived in terms of linear matrix inequalities (LMIs) and a technique for the estimation of the uncertainty bound is proposed by solving a generalized eigenvalue minimization problem. The problem of robust controller synthesis is concerned with designing a feedback controller such that the resulting closed-loop system is gradient-like for all admissible uncertainties. It is shown that a solution to the gradient-like control problem for the uncertain pendulum-like system can be obtained by solving a gradient-like control problem for an uncertainty free system. An example is presented to demonstrate the applicability and validity of the proposed approach.