On passivity, feedback passivity, and feedback passivity over erasure network: a piecewise affine approximation approach

Abstract

In this paper, we deal with the problem of local passivity and local feedback passivation of smooth discrete-time nonlinear systems by considering their piecewise affine approximations. Sufficient conditions are derived for local passivity and local feedback passivity. These results are then extended to systems that operate over Gilbert-Elliott type communication channels. One of the main features of the approach presented in this paper is that it allows us to design the controller by solving a few linear matrix inequalities (LMIs) that are subject to certain constraints. As a special case, results for feedback passivity of piecewise affine systems over a lossy channel are also derived.