Piecewise linear switched dynamical systems: A review

Towards Theory of Piecewise Linear Dynamical Systems ⋆

In this paper, we consider a planar dynamical system with a piecewise linear function containing an arbitrary number (but finite) of dropping sections and approximating some continuous nonlinear function. Studying all possible local and global bifurcations of its limit cycles, we prove that such a piecewise linear dynamical system with k dropping sections and 2k + 1 singular points can have at ...

Piecewise Constant Switched Dynamical Systems in Power Electronics

This paper overviews nonlinear dynamics of switching power converters which are common objects in dynamical system theory and power electronics. First, complex dynamics of single switching power converters is discussed. Their nonlinear switching can cause rich chaotic and bifurcation phenomena including complicated superstable periodic behavior in discontinuous conduction mode. Second, parallel...

Piecewise Constant Controlled Linear Fuzzy Systems

A survey on piecewise-linear models of regulatory dynamical systems

Recent developments in understanding the various regulatory systems, especially the developments in biology and genomics, stimulated an interest in modelling such systems. Hybrid systems, originally developed for process control applications, provide advances in modelling such systems.A particular class of hybrid systems which are relatively simpler to analyze mathematically but still capable o...

Robust Model Predictive Control for Switched Piecewise Linear Hybrid Systems

This paper investigates the robust tracking and regulation control problems for discrete-time, switched piecewise linear hybrid systems affected by parameter variations. In particular, the main question addressed is related to the existence of a controller such that the closedloop system exhibits an attainable desired behavior under all possible parameter variation. Checking attainability and c...