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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
##### Keywords:
delay; perturbations; Lyapunov function; robust stabilization
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