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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

x ˙=(A+ΔA(t))x(t)+ 0 r B i u i (t-h i )+ 0 r ΔB j (t)u j (t-h ˜ j )


A(t)=DF(t)E,B j (t)=D j F j (t)E j ,|F(t)|1,|F j (t)|<1·

The procedure is as follows: first the linear transformation

z(t)=x(t)+ 0 r t-h i t e A(t-h i -θ) B i u i (θ)dθ

is used, then the robustly stabilizing feedback is designed using an appropriate quadratic Lyapunov functional.

93D21Adaptive or robust stabilization
93C23Systems governed by functional-differential equations
93D30Scalar and vector Lyapunov functions
34K17Transformation and reduction of functional-differential equations and systems; normal forms
93C05Linear control systems