Forwarding stabilization in discrete time

Abstract

The paper deals with stabilization of discrete-time cascade dynamics. The notion of average passivity introduced by the authors is used to achieve stability through an iterative design procedure for feedforward cascaded connections. Academic simulated examples illustrate the performances and compare the proposed solution with the one available in the literature.

Total stability of equilibria motivates integral action in discrete-time nonlinear systems

“…This disproves some arguments of [11]. Finally, we link the obtained results on robust stability to the robust output regulation problem, building on recent forwarding techniques [20]. We justify the addition of an integral action for rejecting constant disturbances or tracking constant references.…”

Repetitive control design based on forwarding for nonlinear minimum-phase systems

“…Nevertheless, a proper discretization of the proposed infinite-dimensional scheme surely deserves of further research, since different approaches can be employed, such as the use of low-pass filters [1,17,18], Fourier approximations [19] [22], [20] or discrete-delay representations [3,6,10]. It is worth stressing, that the proposed approach also opens the doors for new results in RC-design for discrete-time nonlinear systems, possibly combining recent results in forwarding stabilization [34].…”

Discrete-time energy-balance passivity-based control

“…Solving such implicit equality with respect to u may be a difficult problem unavoidable in discrete time. Approximate bounded solutions efficient for preserving stabilization can be easily computed as proposed in Mattioni et al (2019); Mazenc and Nijmeijer (1998).…”