We propose a new technique for the design of state feedback controller for piecewise-linear systems, such that, the closed-loop systems are well-posed and asymptotically stable. First, a new criterion for the avoidance of sliding motion on the boundaries is presented. Then, the piecewise affine controller is constructed in a way such that the resulting closed-loop system satisfies the proposed ...

A technique will be discussed in order to find an estimation of the basin of attraction for each stable equilibrium point in cellular neural networks. The technique is based on the determination of the direction of the trajectories for each of the regions in which the state space is divided via the piecewise linear output function of each cell.

The analysis of complex nonlinear systems is often carried out using simpler piecewise linear representations of them. A principled and practical technique is proposed to linearize and evaluate arbitrary continuous nonlinear functions using polygonal (continuous piecewise linear) models under the L1 norm. A thorough error analysis is developed to guide an optimal design of two kinds of polygona...

The α-reformulation (αR) technique can be used to transform any nonconvex twice-differentiable mixedinteger nonlinear programming problem to a convex relaxed form. By adding a quadratic function to the nonconvex function it is possible to convexify it, and by subtracting a piecewise linearization of the added function a convex underestimator will be obtained. This reformulation technique is imp...