Optimal structurally partitioned filter for undisturbable stochastic systems Part II. Stability and its asymptotic behaviour

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Abstract

This paper investigates the stability of an optimal structurally partitioned filter and its asymptotic behaviour in undisturbable stochastic systems. In fact, these filters cannot assure the exponential asymptotic stability and therefore cannot proceed directly to the steady state problem because they include a fixed point smoother as one estimation mechanism in the parallel processors. It is shown, howover, that these types of estimator are asymptotically stable in the Lyapunov sense by introducing a generalized disturbability (or controllability) matrix (Anderson 1971). It is also shown that after analysing the asymptotic behaviour of such filters, a steady state partitioned filter, which takes the gains as the practical constant, is able to generate the unbiased estimate.

Original languageEnglish
Pages (from-to)1159-1169
Number of pages11
JournalInternational Journal of Systems Science
Volume14
Issue number10
DOIs
Publication statusPublished - 1983
Externally publishedYes

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Stochastic systems
Asymptotic stability
Stochastic Systems
Asymptotic Behavior
Filter
Controllability
Exponential Asymptotic Stability
Parallel Processors
Asymptotically Stable
Lyapunov
Fixed point
Estimator
Asymptotic behavior
Estimate

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Management Science and Operations Research

Cite this

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AB - This paper investigates the stability of an optimal structurally partitioned filter and its asymptotic behaviour in undisturbable stochastic systems. In fact, these filters cannot assure the exponential asymptotic stability and therefore cannot proceed directly to the steady state problem because they include a fixed point smoother as one estimation mechanism in the parallel processors. It is shown, howover, that these types of estimator are asymptotically stable in the Lyapunov sense by introducing a generalized disturbability (or controllability) matrix (Anderson 1971). It is also shown that after analysing the asymptotic behaviour of such filters, a steady state partitioned filter, which takes the gains as the practical constant, is able to generate the unbiased estimate.

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