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First Harmonic Analysis of Linear Control Systems with High-Gain Saturating Feedback

1997; World Scientific; Volume: 07; Issue: 11 Linguagem: Inglês

10.1142/s0218127497001679

1793-6551

Baltazar Aguirre, José Álvarez‐Ramírez, Guillermo A. Fernández, Rodolfo Suárez,

Nonlinear Dynamics and Pattern Formation

A first harmonic approach (describing function method) is used in this work to study the behavior of linear control systems with a saturating high-gain linear feedback. It is shown that when the eigenvalues of the closed-loop system are located deeper in the left-half complex plane, several unstable periodic orbits shrink to the origin, thus leading to an unstable equilibrium point. This dynamical behavior is interpreted as the vanishing of the region of attraction of the origin when a saturating high-gain feedback is used.