scholarly journals Descriptor fractional discrete-time linear system with two different fractional orders and its solution

2016 ◽  
Vol 64 (1) ◽  
pp. 15-20 ◽  
Author(s):  
Ł. Sajewski
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Discrete Time ◽  
Decomposition Theorem ◽  
State Equation ◽  
The State ◽  
Extension Method ◽  
Numerical Example ◽  
Fractional Orders ◽  
Time Linear

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.

scholarly journals Stabilization of positive descriptor fractional discrete-time linear system with two different fractional orders by decentralized controller

2017 ◽  
Vol 65 (5) ◽  
pp. 709-714 ◽  
Author(s):  
Ł. Sajewski
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Positive Systems ◽  
Numerical Example ◽  
Necessary And Sufficient ◽  
Fractional Orders ◽  
Time Linear

Abstract Positive 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.

scholarly journals Minimum Energy Control of Descriptor Fractional Discrete–Time Linear Systems with Two Different Fractional Orders

2017 ◽  
Vol 27 (1) ◽  
pp. 33-41 ◽  
Author(s):  
Łukasz Sajewski
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Minimum Energy ◽  
Decomposition Theorem ◽  
State Equation ◽  
Energy Control ◽  
Minimum Energy Control ◽  
Reachability Condition ◽  
Fractional Orders ◽  
Time Linear

Abstract Reachability and minimum energy control of descriptor fractional discrete-time linear systems with different fractional orders are addressed. Using the Weierstrass–Kronecker decomposition theorem of the regular pencil, a solution to the state equation of descriptor fractional discrete-time linear systems with different fractional orders is given. The reachability condition of this class of systems is presented and used for solving the minimum energy control problem. The discussion is illustrated with numerical examples.

scholarly journals Drazin inverse matrix method for fractional descriptor discrete-time linear systems

2016 ◽  
Vol 64 (2) ◽  
pp. 395-399 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Matrix Method ◽  
Initial Conditions ◽  
State Equation ◽  
The State ◽  
Drazin Inverse ◽  
State Equations ◽  
Numerical Example ◽  
Time Linear

Abstract The Drazin inverse of matrices is applied in order to find the solutions of the state equations of fractional descriptor discrete-time linear systems. The solution of the state equation is derived and the set of consistent initial conditions for a given set of admissible inputs is established. The proposed method is illustrated by a numerical example.

Stability analysis of continuous-time linear systems consisting of n subsystems with different fractional orders

2012 ◽  
Vol 60 (2) ◽  
pp. 279-284 ◽  
Author(s):  
M. Busłowicz
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
State Equation ◽  
The State ◽  
Natural Order ◽  
State Variables ◽  
The Stability ◽  
Derivatives Of ◽  
Fractional Orders ◽  
Time Linear

Abstract. The stability problem of continuous-time linear systems described by the state equation consisting of n subsystems with different fractional orders of derivatives of the state variables has been considered. The methods for asymptotic stability checking have been given. The method proposed in the general case is based on the Argument Principle and it is similar to the modified Mikhailov stability criterion known from the stability theory of natural order systems. The considerations are illustrated by numerical examples.

scholarly journals SINGULAR FRACTIONAL CONTINUOUS-TIME AND DISCRETE-TIME LINEAR SYSTEMS

2013 ◽  
Vol 7 (1) ◽  
pp. 26-33 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
State Equation ◽  
Electrical Circuit ◽  
The State ◽  
Continuous Time Systems ◽  
Definition Of ◽  
Time Systems ◽  
Time Linear

Abstract New classes of singular fractional continuous-time and discrete-time linear systems are introduced. Electrical circuits are example of singular fractional continuous-time systems. Using the Caputo definition of the fractional derivative, the Weierstrass regular pencil decomposition and Laplace transformation the solution to the state equation of singular fractional linear systems is derived. It is shown that every electrical circuit is a singular fractional systems if it contains at least one mesh consisting of branches with only ideal supercondensators and voltage sources or at least one node with branches with supercoils. Using the Weierstrass regular pencil decomposition the solution to the state equation of singular fractional discrete-time linear systems is derived. The considerations are illustrated by numerical examples.

scholarly journals Application of the Drazin inverse to the analysis of descriptor fractional discrete-time linear systems with regular pencils

2013 ◽  
Vol 23 (1) ◽  
pp. 29-33 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Initial Conditions ◽  
The State ◽  
Drazin Inverse ◽  
State Equations ◽  
Numerical Example ◽  
Discrete Time Systems ◽  
Time Systems ◽  
Time Linear

The Drazin inverse of matrices is applied to find the solutions of the state equations of descriptor fractional discrete-time systems with regular pencils. An equality defining the set of admissible initial conditions for given inputs is derived. The proposed method is illustrated by a numerical example.

scholarly journals Design of regular positive and stable descriptor systems via state-feedbacks for descriptor continuous-time linear systems with singular pencils

2014 ◽  
Vol 24 (3) ◽  
pp. 289-297
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Special Form ◽  
The State ◽  
New Method ◽  
Descriptor Systems ◽  
Descriptor System ◽  
Asymptotically Stable ◽  
Numerical Example ◽  
Time Linear

Abstract A new method is proposed of design of regular positive and asymptotically stable descriptor systems by the use of state-feedbacks for descriptor continuous-time linear systems with singular pencils. The method is based on the reduction of the descriptor system by elementary row and column operations to special form. A procedure for the design of the state-feedbacks gain matrix is presented and illustrated by a numerical example

scholarly journals Eigenvalue assignment in fractional descriptor discrete-time linear systems

2017 ◽  
Vol 27 (1) ◽  
pp. 119-128
Author(s):  
Tadeusz Kaczorek ◽  
Kamil Borawski
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Existence Of A Solution ◽  
Numerical Example ◽  
Necessary And Sufficient ◽  
Time Linear ◽  
Eigenvalue Assignment

Abstract The problem of eigenvalue assignment in fractional descriptor discrete-time linear systems is considered. Necessary and sufficient conditions for the existence of a solution to the problem are established. A procedure for computation of the gain matrices is given and illustrated by a numerical example.

scholarly journals Descriptor fractional linear systems with regular pencils

2013 ◽  
Vol 23 (2) ◽  
pp. 309-315 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Laplace Transform ◽  
Linear Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
The State ◽  
Transition Matrices ◽  
State Equations ◽  
Numerical Examples ◽  
The Laplace Transform ◽  
Time Linear

Methods for finding solutions of the state equations of descriptor fractional discrete-time and continuous-time linear systems with regular pencils are proposed. The derivation of the solution formulas is based on the application of the Z transform, the Laplace transform and the convolution theorems. Procedures for computation of the transition matrices are proposed. The efficiency of the proposed methods is demonstrated on simple numerical examples.

KETEROBSERVASIAN SISTEM LINIER DISKRIT

2015 ◽  
Vol 4 (1) ◽  
pp. 108
Author(s):  
Midian Manurung
Keyword(s):  
Linear System ◽  
Discrete Time ◽  
State Vector ◽  
The State ◽  
Input Vector ◽  
Linear Control ◽  
Time Interval ◽  
Initial State ◽  
Time Invariant ◽  
Time Linear

Given the following discrete time-invariant linear control systems:where x 2 Rnx(t + 1) = Ax(t) + Bu(t);y(t) = Cx(t);is the state vector, u 2 Rmis an input vector, y 2 Rris dened as anoutput, A 2 Rnn, B 2 Rnm, and t 2 Zis dened as time. Linear system is said to beobservable on the nite time interval [t0; t+f] if any initial state xis uniquely determinedby the output y(t) over the same time interval. In order to examine the observabilityof the system, we will use a criteria, that is by determining the observability Gramianmatrix of the system is nonsingular and rank of the observability matrix for the systemis n.

Sign in / Sign up

Export Citation Format

Share Document