Technical Notes and Correspondence Stochastic Robustness of Linear Time-Invariant Control Systems

Robert F. Stengel, Laura R. Ray

Research output: Contribution to journalArticlepeer-review

195 Scopus citations


A simple numerical procedure for estimating the stochastic robustness of a linear time-invariant system is described. Monte Carlo evaluation of the system's eigenvalues allows the probability of instability and the related stochastic root locus to be estimated. This analysis approach treats not only Gaussian parameter uncertainties but non-Gaussian cases, including uncertain-but-bounded variations. Confidence intervals for the scalar probability of instability address computational issues inherent in Monte Carlo simulation. Trivial extensions of the procedure admit consideration of alternate discriminants; thus, the probabilities that stipulated degrees of instability will be exceeded or that closed-loop roots will leave desirable regions can also be estimated. Results are particularly amenable to graphical presentation.

Original languageEnglish (US)
Pages (from-to)82-87
Number of pages6
JournalIEEE Transactions on Automatic Control
Issue number1
StatePublished - Jan 1991

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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