Quadratic filtering for non-Gaussian and not asymptotically stable linear discrete-time systems

2014 ◽  
Author(s):  
Filippo Cacace ◽  
Francesco Conte ◽  
Alfredo Germani ◽  
Giovanni Palombo
Keyword(s):  
Discrete Time ◽  
Asymptotically Stable ◽  
Discrete Time Systems ◽  
Non Gaussian ◽  
Time Systems ◽  
Stable Linear

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.

scholarly journals Analysis and comparison of the stability of discrete-time and continuous-time linear systems

2016 ◽  
Vol 26 (4) ◽  
pp. 551-563
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Asymptotic Stability ◽  
Discrete Time ◽  
Continuous Time ◽  
Asymptotically Stable ◽  
Discrete Time Systems ◽  
Continuous Time Systems ◽  
The Matrix ◽  
Discretization Step ◽  
Time Systems ◽  
Time Linear

Abstract The asymptotic stability of discrete-time and continuous-time linear systems described by the equations xi+1 = Ākxi and x(t) = Akx(t) for k being integers and rational numbers is addressed. Necessary and sufficient conditions for the asymptotic stability of the systems are established. It is shown that: 1) the asymptotic stability of discrete-time systems depends only on the modules of the eigenvalues of matrix Āk and of the continuous-time systems depends only on phases of the eigenvalues of the matrix Ak, 2) the discrete-time systems are asymptotically stable for all admissible values of the discretization step if and only if the continuous-time systems are asymptotically stable, 3) the upper bound of the discretization step depends on the eigenvalues of the matrix A.

scholarly journals Comparison of approximation methods of positive stable continuous-time linear systems by positive stable discrete-time systems

2013 ◽  
Vol 62 (2) ◽  
pp. 345-355 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
Electrical Circuit ◽  
Approximation Methods ◽  
Asymptotically Stable ◽  
Numerical Examples ◽  
Discrete Time Systems ◽  
Time Systems ◽  
Time Linear

Abstract The positive asymptotically stable continuous-time linear systems are approximated by corresponding asymptotically stable discrete-time linear systems. Two methods of the approximation are presented and the comparison of the methods is addressed. The considerations are illustrated by three numerical examples and an example of positive electrical circuit.

scholarly journals Approximation of fractional positive stable continuous-time linear systems by fractional positive stable discrete-time systems

2013 ◽  
Vol 23 (3) ◽  
pp. 501-506 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Asymptotic Stability ◽  
Linear Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
Asymptotically Stable ◽  
Type Approximation ◽  
Discrete Time Systems ◽  
Time Systems ◽  
Time Linear

Abstract Fractional positive asymptotically stable continuous-time linear systems are approximated by fractional positive asymptotically stable discrete-time systems using a linear Padé-type approximation. It is shown that the approximation preserves the positivity and asymptotic stability of the systems. An optional system approximation is also discussed.

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