Incremental Dissipativity based Control of Discrete-Time Nonlinear Systems via the LPV Framework

TL;DR

This paper introduces a convex output-feedback control synthesis method for discrete-time nonlinear systems using the LPV framework, ensuring incremental dissipativity and improved stability over standard approaches.

Contribution

It develops the first convex output-feedback controller design for discrete-time nonlinear systems based on incremental dissipativity within the LPV framework.

Findings

Enhanced stability and performance demonstrated in simulation.

Convex synthesis guarantees incremental dissipativity.

Addresses limitations of naive LPV application to nonlinear systems.

Abstract

Unlike for Linear Time-Invariant (LTI) systems, for nonlinear systems, there exists no general framework for systematic convex controller design which incorporates performance shaping. The Linear Parameter-Varying (LPV) framework sought to bridge this gap by extending convex LTI synthesis results such that they could be applied to nonlinear systems. However, recent literature has shown that naive application of the LPV framework can fail to guarantee the desired asymptotic stability guarantees for nonlinear systems. Incremental dissipativity theory has been successfully used in the literature to overcome these issues for Continuous-Time (CT) systems. However, so far no solution has been proposed for output-feedback based incremental control for the Discrete-Time (DT) case. Using recent results on convex analysis of incremental dissipativity for DT nonlinear systems, in this paper, we propose a convex output-feedback controller synthesis method to ensure closed-loop incremental dissipativity of DT nonlinear systems via the LPV framework. The proposed method is applied on a simulation example, demonstrating improved stability and performance properties compared to a standard LPV controller design.