Incremental Stability and Performance Analysis of Discrete-Time Nonlinear Systems using the LPV Framework

Abstract

The dissipativity framework is widely used to analyze stability and performance of nonlinear systems. By embedding nonlinear systems in an LPV representation, the convex tools of the LPV framework can be applied to nonlinear systems for convex dissipativity based analysis and controller synthesis. However, as has been shown recently in literature, naive application of these tools to nonlinear systems for analysis and controller synthesis can fail to provide the desired guarantees. Namely, only performance and stability with respect to the origin is guaranteed. In this paper, inspired by the results for continuous-time nonlinear systems, the notion of incremental dissipativity for discrete-time nonlinear systems is proposed, whereby stability and performance analysis is done between trajectories. Furthermore, it is shown how, through the use of the LPV framework, convex conditions can be obtained for incremental dissipativity analysis of discrete-time nonlinear systems. The developed concepts and tools are demonstrated by analyzing incremental dissipativity of a controlled unbalanced disk system.

arXiv commentAccepted to 4th IFAC Workshop on Linear Parameter-Varying Systems

References in corpus (3)

• Convex Incremental Dissipativity Analysis of Nonlinear Systems - Extended version
• Pitfalls of Guaranteeing Asymptotic Stability in LPV Control of Nonlinear Systems
• Linear Parameter-Varying Control of Nonlinear Systems based on Incremental Stability

Cited by in corpus (5)

• A Lyapunov function for robust stability of moving horizon estimation
• Convex Incremental Dissipativity Analysis of Nonlinear Systems - Extended version
• Data-driven Dissipativity Analysis of Linear Parameter-Varying Systems
• Robust output feedback model predictive control using online estimation bounds
• Incremental Dissipativity based Control of Discrete-Time Nonlinear Systems via the LPV Framework