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Stabilization of uncertain systems via linear control. (English) Zbl 0554.93054

The paper gives two elementary results on the feedback stability of time- varying systems defined by x ˙=A(q)x+B(q)u, where q is a time- varying parameter. (i) The stability of the system with a linear feedback u=Kx can be decided by a quadratic Lyapunov function if and only if the same is true of the system

y ˙=A0B0y+0Iu;

(ii) If with u=p(x), where p(0)=0 and p is continuously differentiable, the feedback system has a quadratic Lyapunov function, then with u=(p/x) x=0 x it also has a quadratic Lyapunov function.

Reviewer: S.Mossaheb

MSC:
93D15Stabilization of systems by feedback
93C99Control systems, guided systems
93D05Lyapunov and other classical stabilities of control systems
93C05Linear control systems
93D20Asymptotic stability of control systems
34D20Stability of ODE