Necessary and Sufficient Conditions in Terms of Differential-Forms for Linearization of the State Equations up to Input-Output Injections

2010 ◽  
Author(s):  
V. Kaparin ◽  
U. Kotta
Keyword(s):  
Differential Forms ◽  
Sufficient Conditions ◽  
The State ◽  
Necessary And Sufficient Conditions ◽  
Input Output ◽  
State Equations ◽  
Necessary And Sufficient

scholarly journals On controllability and observability of fractional continuous-time linear systems with regular pencils

2017 ◽  
Vol 65 (3) ◽  
pp. 297-304
Author(s):  
A. Younus ◽  
I. Javaid ◽  
A. Zehra
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
The State ◽  
Necessary And Sufficient Conditions ◽  
State Equations ◽  
Necessary And Sufficient ◽  
Controllability And Observability ◽  
Time Linear

AbstractIn this paper necessary and sufficient conditions of controllability and observability for solutions of the state equations of fractional continuous time linear systems with regular pencils are proposed. The derivations of the conditions are based on the construction of Gramian matrices.

P-D Feedback for Decoupling and Pole Assignment of Singular Systems

1998 ◽  
Vol 120 (3) ◽  
pp. 378-388 ◽  
Author(s):  
F. N. Koumboulis ◽  
B. G. Mertzios
Keyword(s):  
Closed Loop ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Pole Assignment ◽  
Loop System ◽  
Necessary And Sufficient Conditions ◽  
Algebraic Equations ◽  
Input Output ◽  
Closed Loop System ◽  
Necessary And Sufficient

The problem of reducing a multi input-multi output system to many single input-single output systems, namely the problem of input-output decoupling, is studied for the case of singular systems i.e., for systems described by dynamic and algebraic equations. The problem of input-output decoupling with simultaneous arbitrary pole assignment, via proportional plus derivative (P-D) state feedback, is extensively solved. The general explicit expression of all P-D controllers solving the decoupling problem is determined. The general form of the diagonal elements of the decoupled closed-loop system is proven to be in a form having a fixed numerator polynomial and an arbitrary denominator polynomial. The necessary and sufficient conditions for the solvability of the problem of decoupling with simultaneous asymptotic stabilizability or arbitrary pole assignment are established. Furthermore, the necessary and sufficient conditions for decoupling with simultaneous impulse elimination, as well as the necessary and sufficient conditions for decoupling with arbitrary assignment of the finite and infinite poles of the closed-loop system, are established.

scholarly journals Zeroing of state variables in fractional descriptor electrical circuits by state-feedbacks

2014 ◽  
Vol 63 (3) ◽  
pp. 321-333
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Closed Loop ◽  
Sufficient Conditions ◽  
The State ◽  
Necessary And Sufficient Conditions ◽  
State Variables ◽  
Electrical Circuits ◽  
Closed Loop Systems ◽  
Necessary And Sufficient

Abstract The problem of zeroing of the state variables in fractional descriptor electrical circuits by state-feedbacks is formulated and solved. Necessary and sufficient conditions for the existence of gain matrices such that the state variables of closed-loop systems are zero for time greater zero are established. The procedure of choice of the gain matrices is demonstrated on simple descriptor electrical circuits with regular pencils

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 Decoupling zeros of positive electrical circuits

2013 ◽  
Vol 62 (4) ◽  
pp. 553-568 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Input Output ◽  
Electrical Circuits ◽  
Necessary And Sufficient

Abstract Necessary and sufficient conditions for the reachability and observability of the positive electrical circuits composed of resistors, coils, condensators and voltage sources are established. Definitions of the input-decoupling zeros, output-decoupling zeros and input-output decoupling zeros of the positive electrical circuits are proposed. Some properties of the decoupling zeros of positive electrical circuits are discussed.

Decoupling zeros of positive continuous-time linear systems

2013 ◽  
Vol 61 (3) ◽  
pp. 557-562 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Input Output ◽  
Necessary And Sufficient ◽  
Time Linear

Abstract Necessary and sufficient conditions for the reachability and observability of the positive continuous-time linear systems are established. Definitions of the input-decoupling zeros, output-decoupling zeros and input-output decoupling zeros are proposed. Some properties of the decoupling zeros are discussed.

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.

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