2,312 publications from this institution
This paper addresses the stability issue for a class of piecewise affine (PWA) systems, where the state spaces are assumed to be dividable into a certain number of hypercuboid subspaces. By constructing appropriate piecewise continuous Lyapunov functions, several numerically tractable stability criteria are developed for four subclasses of such PWA systems, which allow to recast the switching control problem for the PWA systems as a convex optimization problem. Moreover, the proposed method is applied to switching controller design for (globally and locally) stabilizing the unstable equilibrium points of PWA chaotic systems. Numerical simulations on the chaotic Chua's circuit are presented to verify the theoretical results.
As a paradigm for nonlinear spatial-temporal processing, cellular nonlinear networks (CNN) are biologically inspired systems where computation emerges from a collection of simple locally coupled nonlinear cells. Our investigation is an exploration of an important and difficult aspect of implementing arbitrary Boolean functions by using CNN. A typical class of basic key Boolean functions is the class of linearly separable ones. In this paper, we focus on establishing a complete set of mathematical theories for the linearly separable Boolean functions (LSBF) that are identical to a class of uncoupled CNN. First, we obtain an essential relationship between the template and the offset levels as well as the basis of the binary input vector set in the uncoupled CNN. More precisely, we construct a neat binary input–output truth table and some interesting properties of the offset levels of the uncoupled CNN, and develop a practical design formula for the class of CNN template. Especially, we found a criterion for LSBF, which depends only on symbolic relations between a Boolean function's outputs. Furthermore, we develop a method for representing any linearly nonseparable Boolean function into a logic operation of a sequence of linearly separable ones for a small number of inputs.
