Lyapunov functions are an essential tool in the stability analysis of dynamical systems, both
in theory and applications. They provide sufficient conditions for the stability of equilibria or …

Robust chaos is defined by the absence of periodic windows and coexisting attractors in
some neighborhoods in the parameter space of a dynamical system. This unique book …

We present dissipative systems with unstable dynamics called the unstable dissipative
systems which are capable of generating a multi-stable behavior, ie, depending on its initial …

In this paper, we investigate the dynamical behavior of a one-dimensional piecewise map
based on the logistic map, where generalized multistability can be observed. The proposed …

This paper develops a new sampling-based method for stability verification of piecewise
continuous nonlinear systems via Lyapunov functions. Depending on the nonlinear system …

This paper considers the problem of stability verification for discrete-time nonlinear systems
via Lyapunov functions. Depending on the system dynamics, the candidate Lyapunov …

Given an autonomous discrete time system with an equilibrium at the origin and a
hypercube containing the origin, we state a linear programming problem, of which any …

This book is a comprehensive collection of known results about the Lozi map, a piecewise-
affine version of the Henon map. Henon map is one of the most studied examples in …

In this article the solvability analysis of discretetime nonlinear singular switched systems with
restricted switching signals is studied. We provide necessary and sufficient conditions for the …

What kind of dynamics is a piecewise linear system able to display? How may they generate
heteroclinic chaos? How can the coexistence of attractors be designed and characterized …