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Abstract-In this paper we consider spatially distributed heterogeneous discrete-time systems which are interconnected over an infinite lattice. An operator-pencil approach is employed to develop analysis conditions, which are less conservative than those previously available. Synthesis conditions are also obtained and are in the form of operator inequalities. In general these are infinite dimensional but in the case of eventually invariant systems these reduce to a semidefinite program.

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Nonlinear excitation in self gravitating quantum dusty plasma is analysed from the viewpoint of perturbation theory. A plasma configuration consisting of electron, ion and dust particles are treated by reductive perturbation theory, to deduce two coupled modified KdV equations. The soliton like solutions of such coupled systems are obtained with the help of another multiple scale perturbation theory. This leads to the variation of soliton amplitude and velocity due to the several interaction terms.