Discrete-time filtering for linear systems with non-Gaussian initial conditions: asymptotic behavior of the difference between the MMSE and LMSE estimates

1992 ◽  
Vol 37 (1) ◽  
pp. 114-120 ◽  
Author(s):  
R.B. Sowers ◽  
A.M. Makowski
Keyword(s):  
Asymptotic Behavior ◽  
Linear Systems ◽  
Discrete Time ◽  
Initial Conditions ◽  
The Difference ◽  
Non Gaussian

scholarly journals Simple and weak delta-invariant psolyhedral sets for discrete-time singular systems

2003 ◽  
Vol 14 (4) ◽  
pp. 339-347 ◽  
Author(s):  
Eugênio B. Castelan ◽  
Sophie Tarbouriech
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Initial Conditions ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Convex Polyhedra ◽  
Equivalent System ◽  
Positive Invariance ◽  
Regular Linear Systems ◽  
Necessary And Sufficient

In this paper, necessary and sufficient conditions for the positive invariance of convex polyhedra with respect to linear discrete-time singular systems subject to bounded additive disturbances are established. New notions of delta-invariance under different assumptions on the initial conditions are defined. Specifically, the notions of simple and weak delta-invariance are considered. They can be seen as extensions of the delta-positive invariance concept used for the regular linear systems with additive disturbances. The results are presented by considering classical equivalent system representations for linear singular systems.

scholarly journals Global Asymptotic Stability for Linear Fractional Difference Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
A. Brett ◽  
E. J. Janowski ◽  
M. R. S. Kulenović
Keyword(s):  
Asymptotic Behavior ◽  
Asymptotic Stability ◽  
Difference Equation ◽  
Global Asymptotic Stability ◽  
Initial Conditions ◽  
Positive Equilibrium ◽  
Real Numbers ◽  
Fractional Difference ◽  
Fractional Difference Equation ◽  
The Difference

Consider the difference equation xn+1=(α+∑i=0kaixn-i)/(β+∑i=0kbixn-i),  n=0,1,…, where all parameters α,β,ai,bi,  i=0,1,…,k, and the initial conditions xi,  i∈{-k,…,0} are nonnegative real numbers. We investigate the asymptotic behavior of the solutions of the considered equation. We give easy-to-check conditions for the global stability and global asymptotic stability of the zero or positive equilibrium of this equation.

scholarly journals Computation of initial conditions and inputs for given outputs of fractional and positive discrete-time linear systems

2012 ◽  
Vol 22 (2) ◽  
pp. 145-159 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Initial Conditions ◽  
Sufficient Conditions ◽  
Existence Of Solution ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient ◽  
Time Linear

Computation of initial conditions and inputs for given outputs of fractional and positive discrete-time linear systemsThe problem of computation of initial conditions and inputs for given outputs of fractional standard and positive discrete-time linear systems is formulated and solved. Necessary and sufficient conditions for existence of solution to the problem are established. It is shown that there exist the unique solutions to the problem only if the pair (A, C) of the system is observable.

scholarly journals Application of the Drazin inverse to the analysis of descriptor fractional discrete-time linear systems with regular pencils

2013 ◽  
Vol 23 (1) ◽  
pp. 29-33 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Initial Conditions ◽  
The State ◽  
Drazin Inverse ◽  
State Equations ◽  
Numerical Example ◽  
Discrete Time Systems ◽  
Time Systems ◽  
Time Linear

The Drazin inverse of matrices is applied to find the solutions of the state equations of descriptor fractional discrete-time systems with regular pencils. An equality defining the set of admissible initial conditions for given inputs is derived. The proposed method is illustrated by a numerical example.

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