Stability analysis of uncertain feedback systems with multiple time delays and series nonlinearities (Q679230)

The stability of uncertain delay systems of the form \[ \begin{aligned} \dot x(t) &= Ax(t)+ \sum^n_{i=1} A_{di}x(t- h_i)+ D(t)+ \Delta E(x(t),t)+ \sum^n_{i=1} \Delta E_{di}x(t- h_i,t)\\ y(t) &= Cx(t)+\Delta C(x(t),t)\end{aligned} \] is studied and simple delay-independent criteria of the form \(\mu(A)+ K<0\) are derived; i.e. if \(A\) is stable enough, then so is the uncertain delay system if the rest of the system and the uncertainties are small enough. Similar delay-dependent criteria are obtained when \[ \widetilde A= A+\sum^n_{i=1} A_{di} \] of the form \[ \mu(\widetilde A)+ K(h_1,\dots, h_n)<0, \] where \(K\) now depends on the delays.