Stability of lurie-type non-linear equations
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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.
KeywordsControl System Direct Control Linear Case Indirect Control Indirect Control System
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