This article presents conditions for global input-to-state stability (ISS) and stabilization of discrete-time, possibly discontinuous, piecewise affine (PWA) systems. Piecewise quadratic, possibly discontinuous candidate ISS Lyapunov functions are employed for both analysis and synthesis purposes. This enables us to obtain sufficient conditions based on linear matrix inequalities, which can be ...

In this paper we prove existence results for extremal solutions of the first order discontinuous impulsive differential inclusions with periodic boundary conditions and impulses at the fixed times under certain monotonicity conditions of the multi-valued functions.

We address the solution of multiregion elliptic and parabolic problems with strongly discontinuous coefficients across interfaces. The underlying idea is, roughly, to perturb around the infinitely discontinuous coefficient solution, that is, to perturb the solution where one region is a perfect conductor. The result is partial decoupling of the interface conditions. The algorithm requires a sma...

This paper considers discrete-time nonlinear, possibly discontinuous, systems in closed-loop with Model Predictive Controllers (MPC). The aim of the paper is to provide a priori sufficient conditions for asymptotic stability in the Lyapunov sense and robust stability, while allowing for both the system dynamics and the value function of the MPC cost to be discontinuous functions of the state. T...

Managing innovation and particularly searching for new ideas in a steady state environment is different than in discontinuous conditions where traditional practices and routines may prove ineffective. This paper reviews and empirically explores the field of search strategies and practices for discontinuous innovation and, for the first time, tests the validity of the "Discontinuous Innovation (...

This paper is devoted to time domain numerical solutions of twodimensional (2D) material interface problems governed by the transverse magnetic (TM) and transverse electric (TE) Maxwell’s equations with discontinuous electromagnetic solutions. Due to the discontinuity in wave solutions across the interface, the usual numerical methods will converge slowly or even fail to converge. This calls fo...

*Correspondence: [email protected] Departamento de Análise Matemática, Facultade de Matemáticas, Universidade de Santiago de Compostela, Campus Sur, Santiago de Compostela, 15782, Spain Abstract We use a recent Schauder-type result for discontinuous operators in order to look for solutions for first-order differential equations subject to initial functional conditions. We show how this abstr...

A discontinuous change in the size of an attractor is the most easily observed type of global bifurcation. More generally, an explosion is a discontinuous change in the set of recurrent points. An explosion often results from heteroclinic and homoclinic tangency bifurcations. We prove that, for one-dimensional maps, explosions are generically the result of either tangency or saddle-node bifurca...

We provide a unified approach to existence of Nash equilibria in (possibly) discontinuous and qualitative games. We combine the idea of a local continuous selection of each player’s strict upper contour set from the qualitative games literature with the “better reply security” idea (Reny [15]) of activating different players locally from the discontinuous games literature, together with a weak ...