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Robust stabilization of uncertain input-delayed systems using reduction method. (English) Zbl 0969.93035
One considers the problem of feedback stabilization of the uncertain system $$\dot x= (A+\Delta A(t)) x(t)+ \sum^r_0 B_i u_i(t- h_i)+ \sum^r_0 \Delta B_j(t) u_j(t- \widetilde h_j)$$ with $$A(t)= DF(t)E,\quad B_j(t)= D_jF_j(t) E_j,\quad|F(t)|\le 1,\quad|F_j(t)|< 1.$$ The procedure is as follows: first the linear transformation $$z(t)= x(t)+ \sum^r_0 \int^t_{t- h_i} e^{A(t- h_i-\theta)} B_iu_i(\theta) d\theta$$ is used, then the robustly stabilizing feedback is designed using an appropriate quadratic Lyapunov functional.

MSC:
 93D21 Adaptive or robust stabilization 93C23 Systems governed by functional-differential equations 93D30 Scalar and vector Lyapunov functions 34K17 Transformation and reduction of functional-differential equations and systems; normal forms 93C05 Linear control systems
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References:
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