Maximizing the Exponential Decay Rate for Finite Dimensional Bilinear Systems using Passivity-Based Controllers

Passivity-based controllers which ensure the asymptotic stability of the closed-loop system can be developed with the aid of the Krasovskii passivity notion. However, there are no available design procedures to impose a set of performances. The main focus of the current paper is to formulate an optimization problem whose solution provides the parameters of a Krasovskii passivity-based controller (K-PBC) which ensures local exponential stability with a maximized lower bound of the decay rate. After a convexification procedure we obtain a linear programming problem with linear matrix inequality constraints. The numerical example underlines the advantage of the proposed method by emphasizing the differ-ence between an optimized and a default controller obtained without optimization.