Incremental Stability and Performance Analysis of Discrete-Time Nonlinear Systems using the LPV Framework
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.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Convex Equilibrium-Free Stability and Performance Analysis of Discrete-Time Nonlinear Systems
This paper considers the equilibrium-free stability and performance analysis of discrete-time nonlinear systems. We consider two types of equilibrium-free notions. Namely, the universal shifted concept, which considers s…
Contraction Analysis of Discrete-time Stochastic Systems
In this paper, we develop a novel contraction framework for stability analysis of discrete-time nonlinear systems with parameters following stochastic processes. For general stochastic processes, we first provide a suffi…
Closed-Loop Finite-Time Analysis of Suboptimal Online Control
Suboptimal methods in optimal control arise due to a limited computational budget, unknown system dynamics, or a short prediction window among other reasons. Although these methods are ubiquitous, their transient perform…
Model Predictive ControlFormally Verified Neural Lyapunov Function for Incremental Input-to-State Stability of Unknown Systems
This work presents an approach to synthesize a Lyapunov-like function to ensure incrementally input-to-state stability ($\delta$-ISS) property for an unknown discrete-time system. To deal with challenges posed by unknown…
Convex Incremental Dissipativity Analysis of Nonlinear Systems - Extended version
Efficiently computable stability and performance analysis of nonlinear systems becomes increasingly more important in practical applications. Dissipativity can express stability and performance jointly, but existing resu…