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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 \[ A(t)= DF(t)E,\quad B_j(t)= D_jF_j(t) E_j,\quad|F(t)|\leq 1,\quad|F_j(t)|< 1. \] 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 Control/observation systems governed by functional-differential equations
93D30 Lyapunov and storage functions
34K17 Transformation and reduction of functional-differential equations and systems, normal forms
93C05 Linear systems in control theory
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