Abstract. Factional Discrete-time linear systems with fractional different orders are addressed. The Weierstrass-Kronecker decomposition theorem of the regular pencil is extended to the descriptor fractional discrete-time linear system with different fractional orders. Using the extension, method for finding the solution of the state equation is derived. Effectiveness of the method is demonstrated on a numerical example.
PurposeThe purpose of this paper is to study the 2D hybrid linear model, which is a method of describing both continuous‐ and discrete‐time dynamics in one system. Singularity of 2D hybrid linear models is a newly occurred problem and a very important question is how to compute the solution of the singular 2D hybrid linear model.Design/methodology/approachComputation of the solution of mentioned system is based on Laplace transform, Z‐transform and shifting algorithm. The inverse Laplace transform and inverse Z‐transform are used in two cases.FindingsIn this paper, a class of 2D singular hybrid linear systems is introduced. Two methods for computation of solutions of the singular hybrid system with nonzero boundary conditions are proposed. Both methods are illustrated by the examples.Originality/valuePresented methods are a new way for computing the solution of singular 2D hybrid linear systems.
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