scholarly journals Sensitivity Limitations for Multivariable Linear Filtering

2007 ◽  
Vol 2007 ◽  
pp. 1-8
Author(s):  
Steven R. Weller
Keyword(s):  
Half Plane ◽  
Integral Inequality ◽  
Singular Values ◽  
Multivariable Systems ◽  
Linear Filtering ◽  
Transfer Matrices ◽  
Process Noise ◽  
Fundamental Limitations ◽  
Output Noise ◽  
Poles And Zeros

This paper examines fundamental limitations in performance which apply to linear filtering problems associated with multivariable systems having as many inputs as outputs. The results of this paper quantify unavoidable limitations in the sensitivity of state estimates to process and measurement disturbances, as represented by the maximum singular values of the relevant transfer matrices. These limitations result from interpolation constraints imposed by open right half-plane poles and zeros in the transfer matrices linking process noise and output noise with state estimates. Using the Poisson integral inequality, this paper shows how sensitivity limitations and tradeoffs in multivariable filtering problems are intimately related to the directionality properties of the open right half-plane poles and zeros in these transfer matrices.

scholarly journals Autotune identification for systems with right-half-plane poles and zeros

1999 ◽  
Vol 9 (2) ◽  
pp. 161-169 ◽  
Author(s):  
Shih-Haur Shen ◽  
Hong-Den Yu ◽  
Cheng-Ching Yu
Keyword(s):  
Half Plane ◽  
Poles And Zeros

scholarly journals Singular Values of One Parameter Family \(\lambda ((e^{z}-1)/z)^{m}\)

2015 ◽  
Vol 4 (2) ◽  
pp. 295 ◽  
Author(s):  
Mohammad Sajid
Keyword(s):  
Half Plane ◽  
Entire Functions ◽  
Singular Values ◽  
Critical Values ◽  
Parameter Family ◽  
Open Disk ◽  
Left Half ◽  
Left Half Plane

In the present paper, the singular values of one parameter family of entire functions $f_{\lambda}(z)=\lambda\bigg(\dfrac{e^{z}-1}{z}\bigg)^{m}$ and $f_{\lambda}(0)=\lambda$, $m\in \mathbb{N}\backslash \{0\}$, $\lambda\in \mathbb{R} \backslash \{0\}$, $z \in \mathbb{C}$ is investigated. It is shown that all the critical values of $f_{\lambda}(z)$ lie in the left half plane. It is also found that the function $f_{\lambda}(z)$ has infinitely many bounded singular values and lie inside the open disk centered at origin and having radius $|\lambda|$.

scholarly journals Positive stable realizations of fractional continuous-time linear systems

2011 ◽  
Vol 21 (4) ◽  
pp. 697-702 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Minimum Phase ◽  
Transfer Matrices ◽  
Phase Systems ◽  
Poles And Zeros ◽  
Time Linear

Positive stable realizations of fractional continuous-time linear systemsConditions for the existence of positive stable realizations with system Metzler matrices for fractional continuous-time linear systems are established. A procedure based on the Gilbert method for computation of positive stable realizations of proper transfer matrices is proposed. It is shown that linear minimum-phase systems with real negative poles and zeros always have positive stable realizations.

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