Forced oscillations in control systems under near-resonance conditions
The author considers a single-loop control system whose dynamics is described by the differential equation \[ L(d/dt)x = M(d/dt)(f(x) + u(t)) \] where \(L(p)\) and \(M(p)\) are polynomials with constant coefficients, \(\deg L>\deg M \geq 0\), \(f(x)\) is a smooth function and the external action \(u(t)\) is assumed to be \(T\)-periodic. The resonance conditions under which \(L(p)\) has two primitive roots \(\lambda_{1,2} = \pm (2k \pi i)/T\) and the other roots lie left of the imaginary axis are assumed to be satisfied. The new method of multi-sheeted vector guiding functions developed by the author is applied to prove the existence of \(T\)-periodic trajectories for a given system.
scientific article; zbMATH DE number 1290404