Positive realizations of linear systems

Abstract This paper deals with the realization problem of linear systems in which a sign pattern is imposed on the realization{ A b c T }. This problem arises in the context of positive linear systems, i.e. systems in which state variables and the output take nonnegative values whenever initial states and inputs are nonnegative. Using a unitary framework for continuous-time and discrete-time systems we derive necessary and sufficient conditions for positive realizability by means of convex analysis. Moreover, the complete solution in the case of a transfer function of McMillan degree n ⩽ 3 is obtained.

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