scholarly journals Computation of positive realization of MIMO hybrid linear systems in the form of second Fornasini-Marchesini model

2010 ◽  
Vol 20 (3) ◽  
pp. 267-285 ◽  
Author(s):  
Tadeusz Kaczorek ◽  
Łukasz Sajewski
Keyword(s):  
Linear Systems ◽  
Hybrid Systems ◽  
Transfer Matrix ◽  
Sufficient Conditions ◽  
The State ◽  
Realization Problem ◽  
Numerical Example ◽  
State Variable

Computation of positive realization of MIMO hybrid linear systems in the form of second Fornasini-Marchesini modelThe realization problem for positive multi-input and multi-output (MIMO) linear hybrid systems with the form of second Fornasini-Marchesini model is formulated and a method based on the state variable diagram for finding a positive realization of a given proper transfer matrix is proposed. Sufficient conditions for the existence of the positive realization of a given proper transfer matrix are established. A procedure for computation of a positive realization is proposed and illustrated by a numerical example.

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 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

Impulsive finite-time observer design for uncertain positive linear systems with L2-gain analysis

2020 ◽  
Vol 42 (10) ◽  
pp. 1871-1881 ◽  
Author(s):  
Morteza Motahhari ◽  
Mohammad Hossein Shafiei
Keyword(s):  
Linear Systems ◽  
Finite Time ◽  
Estimation Error ◽  
Sufficient Conditions ◽  
The State ◽  
Observer Design ◽  
Linear Matrix ◽  
Time Interval ◽  
State Variables ◽  
L2 Gain

This paper is concerned with the design of a finite-time positive observer (FTPO) for continuous-time positive linear systems, which is robust regarding the L2-gain performance. In positive observers, the estimation of the state variables is always nonnegative. In contrast to previous positive observers with asymptotic convergence, an FTPO estimates positive state variables in a finite time. The proposed FTPO observer, using two Identity Luenberger observers and based on the impulsive framework, estimates exactly the state variables of positive systems in a predetermined time interval. Furthermore, sufficient conditions are given in terms of linear matrix inequalities (LMIs) to guarantee the L2-gain performance of the estimation error. Finally, the performance and robustness of the proposed FTPO are validated using numerical simulations.

Finite Element Analysis With the State Variable Transfer Matrix and Geometric Nonlinearity for Marine Pipelines in Subsurface Tow

1981 ◽  
Vol 103 (1) ◽  
pp. 26-31 ◽  
Author(s):  
W. C. Kan ◽  
A. J. Healey
Keyword(s):  
Transfer Matrix ◽  
Analytical Study ◽  
Numerical Algorithms ◽  
The State ◽  
Stress Distributions ◽  
Element Analysis ◽  
Value System ◽  
State Variable ◽  
Safe Stress ◽  
Buoyancy Forces

An analytical study of subsurface transportation of long marine pipelines has been performed. Systematic models and numerical algorithms are developed to predict the static configuration and stress distributions along the pipeline during transportation phase. A successive linearization technique and the state variable transfer matrix method are utilized to obtain solutions to the nonlinear two-point boundary value system of equations. Discrete buoyancy forces are also included to reduce barge thrust requirement while maintaining safe stress levels along the pipeline.

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 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 Minimum energy control of positive continuous-time linear systems with bounded inputs

2013 ◽  
Vol 23 (4) ◽  
pp. 725-730 ◽  
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 The minimum energy control problem for 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 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.

Necessary and sufficient conditions for stability of fractional discrete-time linear state-space systems

2013 ◽  
Vol 61 (4) ◽  
pp. 779-786 ◽  
Author(s):  
M. Busłowicz ◽  
A. Ruszewski
Keyword(s):  
Asymptotic Stability ◽  
Linear Systems ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
The State ◽  
Necessary And Sufficient Conditions ◽  
Practical Stability ◽  
State Matrix ◽  
Necessary And Sufficient ◽  
Time Linear

Abstract In the paper the problems of practical stability and asymptotic stability of fractional discrete-time linear systems are addressed. Necessary and sufficient conditions for practical stability and for asymptotic stability are established. The conditions are given in terms of eigenvalues of the state matrix of the system. In particular, it is shown that (similarly as in the case of fractional continuous-time linear systems) in the complex plane exists such a region, that location of all eigenvalues of the state matrix in this region is necessary and sufficient for asymptotic stability. The parametric description of boundary of this region is given. Moreover, it is shown that Schur stability of the state matrix (all eigenvalues have absolute values less than 1) is not necessary nor sufficient for asymptotic stability of the fractional discrete-time system. The considerations are illustrated by numerical examples.

scholarly journals Decentralized stabilization of fractional positive descriptor continuous-time linear systems

2018 ◽  
Vol 28 (1) ◽  
pp. 135-140 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Decentralized Stabilization ◽  
Numerical Example ◽  
Necessary And Sufficient ◽  
Descriptor Linear Systems ◽  
Time Linear

AbstractA method for decentralized stabilization of fractional positive descriptor linear systems is proposed. Necessary and sufficient conditions for decentralized stabilization of fractional positive descriptor linear systems are established. The efficiency of the proposed method is demonstrated on a numerical example.

Sign in / Sign up

Export Citation Format

Share Document