scholarly journals Stabilization of Positive Linear Discrete-Time Systems by Using a Brauer’s Theorem

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Begoña Cantó ◽  
Rafael Cantó ◽  
Snezhana Kostova
Keyword(s):  
Discrete Time ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Closed Loop System ◽  
Single Input Single Output ◽  
Single Output ◽  
Discrete Time Systems ◽  
Single Input ◽  
Linear State ◽  
Time Systems

The stabilization problem of positive linear discrete-time systems (PLDS) by linear state feedback is considered. A method based on a Brauer’s theorem is proposed for solving the problem. It allows us to modify some eigenvalues of the system without changing the rest of them. The problem is studied for the single-input single-output (SISO) and for multi-input multioutput (MIMO) cases and sufficient conditions for stability and positivity of the closed-loop system are proved. The results are illustrated by numerical examples and the proposed method is used in stochastic systems.

scholarly journals Realization problem for positive linear systems with time delay

2005 ◽  
Vol 2005 (4) ◽  
pp. 455-463 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Time Delay ◽  
Sufficient Conditions ◽  
Realization Problem ◽  
Single Input Single Output ◽  
Single Output ◽  
Discrete Time Systems ◽  
Single Input ◽  
Necessary And Sufficient ◽  
Time Systems ◽  
Proper Rational Function

The realization problem for positive single-input single-output discrete-time systems with one time delay is formulated and solved. Necessary and sufficient conditions for the solvability of the realization problem are established. A procedure for computation of a minimal positive realization of a proper rational function is presented and illustrated by an example.

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 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.

Optimal Nonlinear Estimation of Linear Stochastic Systems: The Multivariable Extension

1996 ◽  
Vol 118 (2) ◽  
pp. 350-353 ◽  
Author(s):  
M. A. Hopkins ◽  
H. F. VanLandingham
Keyword(s):  
Stochastic Systems ◽  
Transfer Functions ◽  
Mimo Systems ◽  
Linear Time ◽  
Nonlinear Method ◽  
Single Input Single Output ◽  
Linear Time Invariant ◽  
Single Output ◽  
Time Invariant ◽  
Time Systems

This paper extends to multi-input multi-output (MIMO) systems a nonlinear method of simultaneous parameter and state estimation that appeared in the ASME JDSM&C (September, 1994), for single-input single-output (SISO) systems. The method is called pseudo-linear identification (PLID), and applies to stochastic linear time-invariant discrete-time systems. No assumptions are required about pole or zero locations; nor about relative degree, except that the system transfer functions must be strictly proper. In the earlier paper, proofs of optimality and convergence were given. Extensions of those proofs to the MIMO case are also given here.

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