Stability of lurie-type non-linear equations

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Summary

Conditions are given for the indirect control system x′=a(x)+bμ, μ′=φ(σ), σ=cTx−ϱμ, to be absolutely stable. These conditions reduce to LaSalle and Lefschetz's in the linear case: a(x)=Ax. The conditions obtained for the stability of the direct control system x′=a(x)+bφ(σ), σ=cTx, reduce also to Lurie's condition in the linear case. The case of the direct control system x′=a(x, t)+bφ(σ), σ=cTx is also investigated.

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Entrata in Redazione il 18 febbraio 1976.

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Somolinos, A.S. Stability of lurie-type non-linear equations. Annali di Matematica 116, 1–15 (1978). https://doi.org/10.1007/BF02413865

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Keywords

  • Control System
  • Direct Control
  • Linear Case
  • Indirect Control
  • Indirect Control System