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 Stability of fractional positive continuous-time linear systems with state matrices in integer and rational powers

2017 ◽  
Vol 65 (3) ◽  
pp. 305-311
Author(s):  
T. Kaczorek
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
The State ◽  
Positive Eigenvalue ◽  
Asymptotically Stable ◽  
Fractional Systems ◽  
The Stability ◽  
Time Linear

AbstractThe stability of fractional standard and positive continuous-time linear systems with state matrices in integer and rational powers is addressed. It is shown that the fractional systems are asymptotically stable if and only if the eigenvalues of the state matrices satisfy some conditions imposed on the phases of the eigenvalues. The fractional standard systems are unstable if the state matrices have at least one positive eigenvalue.

scholarly journals Positive stable realizations for fractional descriptor continuous-time linear systems

2012 ◽  
Vol 22 (3) ◽  
pp. 303-313 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Transfer Matrix ◽  
Continuous Time ◽  
Polynomial Matrix ◽  
Asymptotically Stable ◽  
Numerical Example ◽  
Time Linear

Abstract A method for computation of positive asymptotically stable realizations of fractional descriptor continuous-time linear systems with regular pencil is proposed. The method is based on the decomposition of the improper transfer matrix into strictly proper matrix and a polynomial matrix. A procedure for decomposition of a positive asymptotically stable realization is given and illustrated by a numerical example.

Positive fractional continuous-time linear systems with singular pencils

2012 ◽  
Vol 60 (1) ◽  
pp. 9-12 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Descriptor Systems ◽  
State Variables ◽  
Algebraic Constraints ◽  
Necessary And Sufficient ◽  
Time Linear

Positive fractional continuous-time linear systems with singular pencils A method for checking the positivity and finding the solution to the positive fractional descriptor continuous-time linear systems with singular pencils is proposed. The method is based on elementary row and column operations of the fractional descriptor systems to equivalent standard systems with some algebraic constraints on state variables and inputs. Necessary and sufficient conditions for the positivity of the fractional descriptor systems are established.

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.

Stability of positive fractional switched continuous-time linear systems

2013 ◽  
Vol 61 (2) ◽  
pp. 349-352
Author(s):  
T. Kaczorek
Keyword(s):  
Asymptotic Stability ◽  
Linear Systems ◽  
Continuous Time ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Asymptotically Stable ◽  
Fractional Systems ◽  
Time Linear

Abstract The asymptotic stability of positive fractional switched continuous-time linear systems for any switching is addressed. Simple sufficient conditions for the asymptotic stability of the positive fractional systems are established. It is shown that the positive fractional switched systems are asymptotically stable for any switchings if the sum of entries of every column of the matrices of all subsystems is negative.

scholarly journals Checking of the positivity of descriptor linear systems by the use of the shuffle algorithm

2011 ◽  
Vol 21 (3) ◽  
pp. 287-298 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Equivalent Form ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Descriptor Systems ◽  
State Equations ◽  
Necessary And Sufficient ◽  
Descriptor Linear Systems ◽  
Time Linear

Checking of the positivity of descriptor linear systems by the use of the shuffle algorithmNecessary and sufficient conditions for the positivity of descriptor continuous-time and discrete-time linear systems are established. The shuffle algorithm is applied to transform the state equations of the descriptor systems to their equivalent form for which necessary and sufficient conditions for their positivity have been derived. A procedure for checking the positivity of the descriptor systems is proposed and 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 Drazin inverse matrix method for fractional descriptor continuous-time linear systems

2014 ◽  
Vol 62 (3) ◽  
pp. 409-412 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Matrix Method ◽  
Initial Conditions ◽  
Drazin Inverse ◽  
State Equations ◽  
Numerical Example ◽  
Continuous Time Systems ◽  
Time Systems ◽  
Time Linear

Abstract The Drazin inverse of matrices is applied to find the solutions of the state equations of the fractional descriptor continuous-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 Minimum energy control of fractional positive continuous-time linear systems with bounded inputs

2014 ◽  
Vol 24 (2) ◽  
pp. 335-340 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Control Problem ◽  
Linear Systems ◽  
Continuous Time ◽  
Minimum Energy ◽  
Sufficient Conditions ◽  
Energy Control ◽  
Existence Of A Solution ◽  
Numerical Example ◽  
Minimum Energy Control ◽  
Time Linear

Abstract A minimum energy control problem for fractional positive continuous-time linear systems with bounded inputs is formulated and solved. Sufficient conditions for the existence of a solution to the problem are established. A procedure for solving the problem is proposed and illustrated with 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.

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