All invariant densities of piecewise linear Markov maps are piecewise constant

Piecewise Constant Controlled Linear Fuzzy Systems

piecewise constant controlled linear fuzzy systems

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piecewise constant controlled linear fuzzy systems

Edge-Preserving Piecewise Linear Image Smoothing Using Piecewise Constant Filters

Most image smoothing filters in the literature assume a piecewise constant model of smoothed output images. However, the piecewise constant model assumption can cause artifacts such as gradient reversals in applications such as image detail enhancement, HDR tone mapping, etc. In these applications, a piecewise linear model assumption is more preferred. In this paper, we propose a simple yet ver...

Dynamics of Piecewise Linear Discontinuous Maps

In this paper, the dynamics of maps representing classes of controlled sampled systems with backlash are examined. First, a bilinear one-dimensional map is considered, and the analysis shows that, depending on the value of the control parameter, all orbits originating in an attractive set are either periodic or dense on the attractor. Moreover, the dense orbits have sensitive dependence on init...