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Delay-dependent robust stabilization of uncertain state-delayed systems. (English) Zbl 1023.93055
For uncertain delayed system \[ \dot{x}(t)=(A+DF(t)E)x(t)+(A_1+D_1F_1(t)E_1)x(t-h)+ (B+DF(t)E_{a})u(t), \] \[ x(t)=\Phi(t),\qquad t\in[-h,0], \] with various feedback controls: \[ u(t)=Gx(t);u(t)=Gx(t)+G_1x(t-h);u(t)=Gx(t)+\int_{t-h}^{t}G_2(s)x(s) ds, \] delay-dependent robust stabilization conditions are obtained, respectively. A feedback control law is constructed by an algorithm based on convex optimization.

MSC:
93D21 Adaptive or robust stabilization
93C23 Control/observation systems governed by functional-differential equations
90C25 Convex programming
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