scholarly journals A modified state variable diagram method for determination of positive realizations of linear continuous-time systems with delays

2012 ◽  
Vol 22 (4) ◽  
pp. 897-905 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Transfer Matrix ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Transfer Matrices ◽  
Diagram Method ◽  
Numerical Examples ◽  
State Variable ◽  
Continuous Time Systems ◽  
Time Systems

A new modified state variable diagram method is proposed for determination of positive realizations of linear continuoustime systems with delays in state and input vectors. Using the method, it is possible to find a positive realization with reduced numbers of delays for a given transfer matrix. Sufficient conditions for the existence of positive realizations of given proper transfer matrices are established. The proposed method is demonstrated on numerical examples.

scholarly journals Positive stable realizations with system Metzler matrices

2011 ◽  
Vol 21 (2) ◽  
pp. 167-188 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Transfer Matrix ◽  
Continuous Time ◽  
Similarity Transformation ◽  
Transfer Matrices ◽  
Numerical Examples ◽  
Continuous Time Systems ◽  
Metzler Matrix ◽  
Time Systems

Positive stable realizations with system Metzler matricesConditions for the existence of positive stable realizations with system Metzler matrices for linear continuous-time systems are established. A procedure for finding a positive stable realization with system Metzler matrix based on similarity transformation of proper transfer matrices is proposed and demonstrated on numerical examples. It is shown that if the poles of stable transfer matrix are real then the classical Gilbert method can be used to find the positive stable realization.

scholarly journals Determination of positive realizations with reduced numbers of delays or without delays for discrete-time linear systems

2012 ◽  
Vol 22 (4) ◽  
pp. 451-465 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Transfer Function ◽  
Linear Systems ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Diagram Method ◽  
State Variable ◽  
Discrete Time Systems ◽  
Time Systems ◽  
Time Linear

A new modified state variable diagram method is proposed for determination of positive realizations with reduced numbers of delays and without delays of linear discrete-time systems for a given transfer function. Sufficient conditions for the existence of the positive realizations of given proper transfer function are established. It is shown that there exists a positive realization with reduced numbers of delays if there exists a positive realization without delays but with greater dimension. The proposed methods are demonstrated on a numerical example.

scholarly journals Computation of positive realizations for descriptor linear continuous-time systems

2018 ◽  
Vol 19 (12) ◽  
pp. 428-432
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
New Method ◽  
Transfer Matrices ◽  
Continuous Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems ◽  
Time Linear

A new method for computation of positive realizations of given transfer matrices of descriptor linear continuous-time linear systems is proposed. Necessary and sufficient conditions for the existence of positive realizations of transfer matrices are given. A procedure for computation of the positive realizations is proposed and illustrated by examples.

scholarly journals On Controllability of Fractional Continuous-Time Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Mina Ghasemi ◽  
Kameleh Nassiri
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Fractional Systems ◽  
Numerical Examples ◽  
Continuous Time Systems ◽  
Fractional System ◽  
Necessary And Sufficient ◽  
Time Systems

The aim of this paper is to study the controllability of fractional systems involving the Atangana–Baleanu fractional derivative using the Caputo approach. In the first step, the solution of a linear fractional system is obtained. Then, based on the obtained solution, some necessary and sufficient conditions for the controllability of such a system will be presented. Afterwards, the controllability of a nonlinear fractional system will be analyzed, based on these results. Our tool for the presentation of the sufficient conditions of controllability in this part is Schauder fixed point theorem. In the last step, the analytical results are illustrated by numerical examples.

Positive stable realizations of discrete-time linear systems

2012 ◽  
Vol 60 (3) ◽  
pp. 605-616
Author(s):  
T. Kaczorek
Keyword(s):  
Transfer Function ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Asymptotically Stable ◽  
Numerical Examples ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems ◽  
Time Linear

Abstract The problem of existence and determination of the set of positive asymptotically stable realizations of a proper transfer function of linear discrete-time systems is formulated and solved. Necessary and sufficient conditions for existence of the set of the realizations are established. A procedure for computation of the set of realizations are proposed and illustrated by numerical examples.

scholarly journals An Improved Antiwindup Design Using an Anticipatory Loop and an Immediate Loop

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Qing Wang ◽  
Maopeng Ran ◽  
Chaoyang Dong ◽  
Maolin Ni
Keyword(s):  
Linear Matrix Inequalities ◽  
Continuous Time ◽  
Actuator Saturation ◽  
Sufficient Conditions ◽  
The Other ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Continuous Time Systems ◽  
Linear Invariant ◽  
Time Systems

We present an improved antiwindup design for linear invariant continuous-time systems with actuator saturation nonlinearities. In the improved approach, two antiwindup compensators are simultaneously designed: one activated immediately at the occurrence of actuator saturation and the other activated in anticipatory of actuator saturation. Both the static and dynamic antiwindup compensators are considered. Sufficient conditions for global stability and minimizing the inducedL2gain are established, in terms of linear matrix inequalities (LMIs). We also show that the feasibility of the improved antiwindup is similar to the traditional antiwindup. Benefits of the proposed approach over the traditional antiwindup and a recent innovative antiwindup are illustrated with well-known examples.

REALIZATION PROBLEM FOR POSITIVE CONTINUOUS-TIME SYSTEMS WITH DELAYS

2006 ◽  
Vol 06 (02) ◽  
pp. 289-298 ◽  
Author(s):  
KACZOREK TADEUSZ
Keyword(s):  
Continuous Time ◽  
Sufficient Conditions ◽  
Realization Problem ◽  
Single Input Single Output ◽  
Single Output ◽  
Continuous Time Systems ◽  
Single Input ◽  
Minimal Realizations ◽  
Time Systems ◽  
Time Linear

The realization problem for positive, continuous-time linear single-input, single-output systems with delays is formulated and solved. Sufficient conditions for the existence of positive realizations of a given proper transfer function are established. A procedure for computation of positive minimal realizations is presented and illustrated by an example.

scholarly journals Analysis of Positive Linear Continuous–Time Systems Using the Conformable Derivative

2018 ◽  
Vol 28 (2) ◽  
pp. 335-340 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Asymptotic Stability ◽  
Linear System ◽  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Conformable Derivative ◽  
Continuous Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems

Abstract Positive linear continuous-time systems are analyzed via conformable fractional calculus. A solution to a fractional linear system is derived. Necessary and sufficient conditions for the positivity of linear systems are established. Necessary and sufficient conditions for the asymptotic stability of positive linear systems are also given. The solutions of positive fractional linear systems based on the Caputo and conformable definitions are compared.

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