Stability of lurie-type non-linear equations

Summary Conditions are given for the indirect control system x′=a(x)+bμ, μ′=φ(σ), σ=c^Tx−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=c^Tx, reduce also to Lurie's condition in the linear case. The case of the direct control system x′=a(x, t)+bφ(σ), σ=c^Tx is also investigated. Entrata in Redazione il 18 febbraio 1976.