scholarly journals Computation of Positive Realizations for Given Impulse Response Matrices of Discrete-Time Systems

2008 ◽  
Vol 2008 ◽  
pp. 1-9
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Impulse Response ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Discrete Time Systems ◽  
Time Systems

A method is presented for computation of positive realizations for given impulse response matrices of discrete-time systems. Sufficient conditions for the existence of positive realizations are established and a procedure for computation of positive realizations for given impulse response matrices is proposed.

scholarly journals Positive Partial Realization Problem for Linear Discrete-Time Systems

2007 ◽  
Vol 17 (2) ◽  
pp. 165-171 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Impulse Response ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Finite Sequence ◽  
Realization Problem ◽  
Numerical Examples ◽  
Discrete Time Systems ◽  
Time Systems

Positive Partial Realization Problem for Linear Discrete-Time SystemsA partial realization problem for positive linear discrete-time systems is addressed. Sufficient conditions for the existence of its solution are established. A procedure for the computation of a positive partial realization for a given finite sequence of the values of the impulse response is proposed. The procedure is illustrated by four numerical examples.

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.

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.

AN OPTIMIZATION APPROACH TO THE DESIGN OF CONSTRAINED REGULATORS FOR UNCERTAIN DISCRETE-TIME SYSTEMS

2006 ◽  
Vol 15 (03) ◽  
pp. 373-387
Author(s):  
M. VASSILAKI ◽  
G. BITSORIS
Keyword(s):  
Discrete Time ◽  
Sufficient Conditions ◽  
Optimization Approach ◽  
Control Constraints ◽  
Existence Of A Solution ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
And Control ◽  
Time Systems ◽  
State And Control Constraints

In this paper the regulation problem of linear discrete-time systems with uncertain parameters under state and control constraints is studied. In the first part of the paper, two theorems concerning necessary and sufficient conditions for the existence of a solution to this problem are presented. Due to the constructive form of the proof of these theorems, these results can be used to the development of techniques for the derivation of a control law transferring to the origin any state belonging to a given set of initial states while respecting the state and control constraints.

Sliding Mode Control of Discrete-Time Systems

2000 ◽  
Vol 122 (4) ◽  
pp. 793-802 ◽  
Author(s):  
A. Jafari Koshkouei ◽  
A. S. I. Zinober
Keyword(s):  
Sliding Mode Control ◽  
Discrete Time ◽  
Sliding Mode ◽  
Sufficient Conditions ◽  
Control Design ◽  
Continuous Case ◽  
Mode Control ◽  
Discrete Time Systems ◽  
Set Of Points ◽  
Time Systems

In discrete-time systems, instead of having a hyperplane as in the continuous case, there is a countable set of points comprising a so-called lattice; and the surface on which these sliding points lie is the latticewise hyperplane. In this paper the concept of multivariable discrete-time sliding mode is clarified and new sufficient conditions for the existence of the sliding mode are presented. A new control design using the properties of discrete sliding is proposed, and the behavior of the system in the sliding mode is studied. Furthermore, the stabilization of discrete-time systems and an optimal sliding lattice are considered. [S0022-0434(00)02804-5]

scholarly journals Absolute stability of a class of fractional positive nonlinear systems

2019 ◽  
Vol 29 (1) ◽  
pp. 93-98 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
Absolute Stability ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Discrete Time Systems ◽  
The Absolute ◽  
Necessary And Sufficient ◽  
Time Systems

Abstract The positivity and absolute stability of a class of fractional nonlinear continuous-time and discrete-time systems are addressed. Necessary and sufficient conditions for the positivity of this class of nonlinear systems are established. Sufficient conditions for the absolute stability of this class of fractional positive nonlinear systems are also given.

scholarly journals Fractional descriptor standard and positive discrete-time nonlinear systems

2015 ◽  
Vol 63 (3) ◽  
pp. 651-655
Author(s):  
T. Kaczorek
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Linear Part ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Numerical Example ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems

AbstractA method of analysis of the fractional descriptor nonlinear discrete-time systems with regular pencils of linear part is proposed. The method is based on the Weierstrass-Kronecker decomposition of the pencils. Necessary and sufficient conditions for the positivity of the nonlinear systems are established. A procedure for computing the solution to the equations describing the nonlinear systems are proposed and demonstrated on a numerical example.

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