Exponential Rate for Bilinear Systems via Passivity-Based Controllers

The theory of finding a controller using Krasovskii passivity has been recently developed and offers local asymptotic stability guarantees, but with the shortcoming of not considering a methodology to design the controller’s parameters such that certain performances are imposed. The current paper proposes an approach to design first and second order Krasovskii passivity-based controllers (K-PBCs) for plants described via the bilinear system framework, and which ensure local exponential stability with optimized convergence rate. The K-BPC’s parameter design procedure is initially expressed in terms of nonlinear matrix inequalities, followed by a method to convexify the problem via a variable change, leading to a set of linear matrix inequalities (LMIs). A numerical example is presented, underlying the advantages of the proposed procedure.