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Robust stabilization for systems with parametric uncertainty and time delay. (English) Zbl 0978.93068
The following linear dynamical system is considered \[ \dot x(t)= (A+\Delta A)x(t)+ (A_d+\Delta A_d) x(t-\tau_d)+ Bu(t),\quad \tau_d> 0,\tag{1} \]
\[ x(t)= \Phi(t),\qquad t\in [-\tau_d, 0], \] where \[ u(t)= Kx(t)\tag{2} \] is a feedback control; the perturbations \(\Delta A\), \(\Delta A_d\) have the form \[ \Delta A= B_0 FC_0,\quad\Delta A_d= B_d EC_d,\quad M_1\leq F\leq M_2, \] \(B_0\), \(C_0\), \(B_d\), \(C_d\) are fixed matrices, \(F\) is an uncertain symmetric matrix.
On the basis of a Lyapunov function, sufficient conditions for robust stabilization of the uncertain closed-loop system (1), (2), for all \(\Delta A\), \(\Delta A_d\) and \(\tau_d> 0\), are obtained.

MSC:
93D21 Adaptive or robust stabilization
93C23 Control/observation systems governed by functional-differential equations
93D30 Lyapunov and storage functions
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