Stabilization and robustness of non-linear unity-feedback system: factorization approach

Desoer, C.; Kabuli, M.G.

doi:10.1080/00207178808906079

Cited by 19 publications

(1 citation statement)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Assume that N is unambiguous, i.e., if yo E hCz is a branch current vector corresponding to a branch-voltage vector z E hC2, then yo is determined uniquely by z. It is well known that N is unambiguous o the mesh-impedance operator k 4 We will show that if, in addition, we assume that the map = IIX*(A -A , ) X x , -X * ( A -A,)Xx,I) z + yo is Lipschitz continuous, then, considering z and yo 5 IIX*ll IIA -A.II*ll~x, -XX,II 5 II A -A,Il*Ilx, -x2lI.…”

Section: Proofmentioning

confidence: 99%

Sensitivity and robust stability of general input-output systems

Doležal

1991

IEEE Trans. Automat. Contr.

View full text Add to dashboard Cite

We consider a general model of an input-output system that is governed by nonlinear operator equations which relate the input, the state, and the output of the system. This model encompasses feedback systems as a special case. Assuming that the governing equations depend on a parameter A which is allowed to vary in a neighborhood of a nominal value A, in a linear space, we study the dependence of the system behavior on A. We call a system insensitive, if for any fmed input, the output depends continuously on A . Similarly, we say that the system is robust, if it is stable for each A in a neighborhood of A,,. By stability, we essentially mean an , appropriate continuity of the input-output operator.Our results give various sufficient conditions for insensitivity and robustness. The Theorems 1, 2, 5, and 6 represent the main results.As examples illustrating the applications of our theory, we discuss 1) estimating the difference of operator inverses, and the insensitivity and robust stabdity of a 2) Hilbert network, 3) feedback-feedforward system, 4) traditional feedback system, and of a 5) time-varying dynamical system described by a linear vector differential equation on [O,a).

show abstract

Section: Proofmentioning

confidence: 99%