We investigate the computational power of several models of dynamical systems under infinitesimal perturbations of their dynamics. We consider in our study models for discrete and continuous time dynamical systems: Turing machines, Piecewise affine maps, Linear hybrid automata and Piecewise constant derivative systems (a simple model of hybrid systems). We associate with each of these models a ...

‎a full nesterov-todd (nt) step infeasible interior-point algorithm‎ ‎is proposed for solving monotone linear complementarity problems‎ ‎over symmetric cones by using euclidean jordan algebra‎. ‎two types of‎ ‎full nt-steps are used‎, ‎feasibility steps and centering steps‎. ‎the‎ ‎algorithm starts from strictly feasible iterates of a perturbed‎ ‎problem‎, ‎and, using the central path and feasi...

Recent development of contraction theory based analysis of singularly perturbed system has opened the door for inspecting differential behavior of multi timescale systems. In this paper a contraction theory based framework is proposed for stabilization of singularly perturbed systems. The primary objective is to design a feedback controller to achieve bounded tracking error for both standard an...