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This paper presents a fairly complete treatment of stability and controllability of piecewise-linear systems defined on a conic partition of R2. This includes necessary and sufficient conditions for stability and controllability, as well as establishing that controllability implies stabilizability by piecewise-linear state feedback. A key tool in the approach is the study of the Poincare map.
We characterize the equivalence of single-input, single-output, discrete-time nonlinear systems to linear ones, via a state coordinate change and with or without feedback. Four cases are distinguished by allowing or disallowing feedback as well as by including the output map or not; the interdependence of these problems is analyzed. An important feature which distinguishes these discrete-time problems...
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