We describe a new class of positive linear discrete-time switching systemsfor which the problems of stability or stabilizability can be resolvedconstructively. This class generalizes the class of systems with independentlyswitching state vector components. The distinctive feature of this class isthat, for any system from this class, its components or blocks can bearbitrarily connected in parallel or in series without loss of the`constructive resolvability' property. It is shown also that, for such systems,it is possible to build constructively the individual positive trajectorieswith the greatest or the lowest rate of convergence to the zero.
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