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The purpose of the paper is to propose a new method for checking the positivity and asymptotic stability of descriptor continuous‐time and discrete‐time linear systems.

The proposed method is based on the elementary operations applied to descriptor linear systems with regular pencils.

The descriptor systems with regular pencils are transformed to equivalent standard systems which are used for checking of the asymptotic stability of descriptor systems.

The paper proposes a new method for investigation of the positivity and asymptotic stability of descriptor continuous‐time and discrete‐time linear systems.

The purpose of this paper is to introduce a new class of fractional positive continuous‐time and discrete‐time linear systems.

Solutions to the state equations of the fractional systems are given.

Necessary and sufficient conditions are established for the internal and external positivity and of the reachability and controllability to zero of the fractional systems.

A method for analysis of the fractional positive linear systems is proposed.

The purpose of this paper is to introduce a new class of positive two‐dimensional (2D) fractional linear systems.

A notion (concept) of order 2D difference is proposed and the solution to the state equations is given.

The classical Cayley‐Hamilton theorem is extended to the positive 2D fractional linear systems. Necessary and sufficient conditions for the positivity of 2D fractional linear systems, reachability and controllability to zero are established.

A method for analysis of positive 2D fractional linear systems is proposed.

The paper aims to formulate and solve the realization problem for 2D positive multi‐input multi‐output linear hybrid systems.

A procedure is proposed for finding a positive 2D realization of a given proper transfer matrix.

Sufficient conditions for the existence of a positive 2D realization of a given proper transfer matrix are established.

A method for computation of a positive 2D realization of a given proper transfer matrix is proposed.

Aims to formulate and solve the minimal positive realization problem for discrete‐time linear single‐input, single‐output systems with many state time‐delays.

A conceptual discussion and approach are taken.

Sufficient conditions for the existence of positive realizations of a given proper rational function are established. A procedure for computation of minimal positive realizations is presented and illustrated by an example.

Extends an earlier method for positive discrete‐time systems with many state time‐delays.

The purpose of this paper is to formulate and solve the pointwise completeness and pointwise degeneracy of standard and positive 2D Fornasini‐Marchesini and 2D Roesser models.

A procedure is proposed for investigation of the pointwise completeness and pointwise degeneracy of 2D standard and positive Fornasini‐Marchesini and Roesser models.

Necessary and sufficient conditions for pointwise completeness and pointwise degeneracy of standard and positive Fornasini‐Marchesini and Roesser models are established.

The paper proposes a method for investigation of the pointwise completeness and pointwise degeneracy of the standard and positive Fornasini‐Marchesini and Roesser models.

The purpose of this paper is to formulate and solve the minimum energy control problem of descriptor positive discrete-time linear systems.

A procedure for computation of the optimal input sequences and the minimal value of the performance index is proposed.

Necessary and sufficient conditions for the positivity and reachability of descriptor positive discrete-time linear systems and sufficient conditions for the existence of solution to the minimum energy control problem are given.

A method for solving of the minimum energy control problem of descriptor positive discrete-time linear systems is proposed.