Towards a Constructive Interconnection and Damping Assignment Stabilization Methodology

International audienceInterconnection and damping assignment passivity-based control (IDA-PBC) relies on the solution of a partial differential equation (PDE) that identifies the assignable storage function [10] [12], thus the difficulties in solving the PDE are usually the main stumbling block that hampers the application of IDA-PBC. The main objective of this paper is to propose a new IDA-PBC to simplify the solution of the PDE, in particular, we extend this method in the following directions. Firstly, we allow the desired interconnection and damping matrices to depend on the control signal, giving the possibility to simplify the PDE to ensure its solvability. Secondly, the PDE directly generates the control signal that has, in general, a simpler expression. Thirdly, it is applicable for general nonlinear systems possibly not affine in the control. The methodology is validated with two illustrative examples