Robust prevention of limit cycle for nonlinear control systems with parametric uncertainties both in the linear plant and nonlinearity

Limit Cycle Predictions of Nonlinear Multivariable Feedback Control Systems with Large Transportation Lags

“…For specified value of frequency ω, the value of N 1 (a 1 ) can be found by solving (21); the corresponding value of N 2 (a 2 ) can be found by (17) or (19). Similarly, N 1 (a 1 ) can be found form (18) or (20) for N 2 (a 2 ) is found by (22).…”

“…In general, real and imaginary parts of the characteristic equation are used as two simultaneous equations to find the solution of the limit cycle for single-input singleoutput (SISO) nonlinear feedback control systems [11][12][13][14][15][16][17]. Therefore, single nonlinearity in the system can be solved easily to find two parameters, that is, oscillation amplitude (A) and frequency (ω) of a limit cycle.…”

Inducing sustained oscillations in feedback-linearizable single-input nonlinear systems

“…Besides the fundamental scientific interest in mathematical systems theory, the design of systems exhibiting driven sustained oscillations remains an important strategic domain of research in the context of applied science. Indeed, oscillators are a common concern of mechanical engineering, electrical engineering, electromechanical engineering, and combustion engineering, as well as in robotics and power electronics (e.g., [1][2][3][4][5][6][7][8][9]). Moreover, the current excitement about microelectromechanical systems (MEMS), and the rise of synthetic biology, calls for the rational design of robust oscillators grounded in an in-depth understanding of both natural and artificially regulated oscillatory dynamical systems (e.g., [10][11][12][13][14][15][16]).…”