The focal point of this paper is a new result on the probabilistic robustness of a stochastic first order filter. For a first order filter transfer function, G(s,/spl tau/), we allow a class of probability distributions /spl phi/ for the time constant /spl tau/ and consider the following question: Given frequency /spl omega//spl ges/0 and unknown probability distribution f /spl isin/ F, to what extent can the expected filter gain g(/spl omega/,/spl tau/)=|G(j/spl omega/,/spl tau/)| deviate from some desired nominal value, g(/spl omega/, /spl tau//sub 0/)? It turns out that the deviations of concern are surprisingly low. For example, with 20% variation in /spl tau/, the expected filter gain deviates from g(/spl omega/,/spl tau//sub 0/) by no more than 0.4% of the zero frequency gain. In addition to performance bounds such as this, we also provide a so-called universal figure of merit. The word "universal" is used because the performance bound attained holds independently of the nominal /spl tau//sub 0/. The frequency /spl omega//spl ges/0 and the admissible probability distributions d/spl isin/F.
[1]
Robert Spence,et al.
Tolerance Design of Electronic Circuits
,
1997
.
[2]
R. Tempo,et al.
Radially truncated uniform distributions for probabilistic robustness of control systems
,
1997,
Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).
[3]
B. R. Barmish,et al.
Probabilistic robustness: an RLC circuit realization of the truncation phenomenon
,
1998,
Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).
[4]
B. Ross Barmish,et al.
The uniform distribution: A rigorous justification for its use in robustness analysis
,
1996,
Math. Control. Signals Syst..
[5]
Stephen W. Director,et al.
Statistical circuit design : a somewhat biased survey
,
1981
.
[6]
G. Hachtel.
The simplicial approximation approach to design centering
,
1977
.