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Semidefinite Lyapunov functions stability and stabilization. (English) Zbl 0868.93048
The paper gives some weakening of the basic Lyapunov theorems by obtaining stability and asymptotic stability for nonnegatively definite Lyapunov functions. These results allow simpler proofs for some previously known results and some extension of the stabilization results for systems that are affine in the control.

MSC:
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
34D20 Stability of solutions to ordinary differential equations
93D15 Stabilization of systems by feedback
93D30 Lyapunov and storage functions
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