AbstractPositive descriptor fractional discrete-time linear systems with fractional different orders are addressed in the paper. The decomposition of the regular pencil is used to extend necessary and sufficient conditions for positivity of the descriptor fractional discrete-time linear system with different fractional orders. A method for finding the decentralized controller for the class of positive systems is proposed and its effectiveness is demonstrated on a numerical example.

The article presents developed method and general principles of creating ladder diagrams, which are commonly used for systems with programmable logic controllers (PLC). Ladder diagrams are created for sequential control systems of technological processes, which are described by a connection pattern, time diagrams of the executive elements` operation. The executive elements are double-acting pneumatic or hydraulic actuators controlled by bistable electrovalves. A method of designing sequential systems enabling the creation of a ladder electro-pneumatic system is presented. The ladder diagram consists of two parts. One is responsible for controlling the valve coils, the other for the implementation of the memory block. The signals that control the transition to the next state are the signals described on the boundaries of the graph division. The synthesis of control systems and their verification was carried out using the computer aided program FluidSim by Festo.