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

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.

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 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.

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.

Optimal Singular Solutions for Linear Multi-Input Systems

1966 ◽  
Vol 88 (2) ◽  
pp. 323-328 ◽  
Author(s):  
R. A. Rohrer ◽  
M. Sobral
Keyword(s):  
Sufficient Conditions ◽  
Singular Control ◽  
Open Loop ◽  
The State ◽  
Singular Solutions ◽  
Linear Feedback ◽  
State Variables ◽  
Performance Indices ◽  
Explicit Formulae ◽  
Necessary And Sufficient

Linear, stationary systems with multiple inputs when subject to performance indices quadratic in the state variables, but explicitly independent of the control variables, may be optimally governed by singular control. Necessary and sufficient conditions for the optimality of both partially singular control and totally singular control are obtained. Moreover, explicit formulae are presented for both open-loop and linear-feedback implementations of the optimal singular control.

scholarly journals Stability conditions for linear continuous-time fractional-order state-delayed systems

2016 ◽  
Vol 64 (1) ◽  
pp. 3-7
Author(s):  
M. Busłowicz
Keyword(s):  
Asymptotic Stability ◽  
Fractional Order ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
The State ◽  
Necessary And Sufficient Conditions ◽  
Order System ◽  
State Matrix ◽  
The Stability ◽  
Necessary And Sufficient

Abstract The stability problem of continuous-time linear fractional order systems with state delay is considered. New simple necessary and sufficient conditions for the asymptotic stability are established. The conditions are given in terms of eigenvalues of the state matrix and time delay. It is shown that in the complex plane there exists such a region that location in this region of all eigenvalues of the state matrix multiplied by delay in power equal to the fractional order is necessary and sufficient for the asymptotic stability. Parametric description of boundary of this region is derived and simple new analytic necessary and sufficient conditions for the stability are given. Moreover, it is shown that the stability of the fractional order system without delay is necessary for the stability of this system with delay. The considerations are illustrated by a numerical example.

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.

scholarly journals Positivity of Fractional Descriptor Linear Discrete–Time Systems

2019 ◽  
Vol 29 (2) ◽  
pp. 305-310
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Discrete Time ◽  
Sufficient Conditions ◽  
State Equation ◽  
The State ◽  
Necessary And Sufficient Conditions ◽  
Numerical Examples ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems

Abstract The positivity of fractional descriptor linear discrete-time systems is investigated. The solution to the state equation of the systems is derived. Necessary and sufficient conditions for the positivity of fractional descriptor linear discrete-time systems are established. The discussion is illustrated with numerical examples.

Sign in / Sign up

Export Citation Format

Share Document