Stabilization of oscillations by a nonnegative feedback control

The feedback stabilization of m-dimensional nonlinear systems is studied in this note. The Jacobian is assumed to possess 2q purely imaginary eigenvalues and m-2q eigenvalues with negative real parts. The feedback control law is assumed to be nonnegative and given by the square of a linear function. The direct and indirect control systems are investigated. In both cases stabilizability is proved and explicit formulas for the feedback functions are obtained. Lyapunov's direct method is employed.<
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