This paper studies inducing robust stable oscillations in nonlinear systems of any order. This goal is achieved through creating stable limit cycles in the closed-loop system. For this purpose, the Lyapunov stability theorem which is suitable for stability analysis of the limit cycles is used. In this approach, the Lyapunov function candidate should have zero value for all the points of the limit cycle and be positive in the other points in the vicinity of it. The proposed robust controller consists of a nominal control law with an additional term that guarantees the robust performance. It is proved that the designed controller results in creating the desirable stable limit cycle in the phase trajectories of the uncertain closed-loop system and leads to induce stable oscillations in the system's output. Additionally, in order to show the applicability of the proposed method, it is applied on two practical systems: a time-periodic microelectromechanical system (MEMS) with parametric errors and a single-link flexible joint robot in the presence of external disturbances. Computer simulations show the effective robust performance of the proposed controllers in generating the robust output oscillations.

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Summary This paper studies on generating periodic behaviors through shaping stable limit cycles in multiple‐input‐multiple‐output nonlinear systems. For this purpose, first, limit cycles are shaped with respect to the desired sustained oscillations of the system's outputs. Then, the Lyapunov analyses, which are appropriate for stability analysis of invariant sets, are employed to design the control law and conclude the asymptotic convergence toward the predefined limit cycles. The problem is studied in two cases. In the first case, some assumptions in the mathematical model are assumed that leads to simplification in the design procedure. In the second case, the design procedure is discussed in more general cases. Finally, the validity and performance of the proposed method for shaping limit cycles with different geometric shapes are illustrated by computer simulations for practical and numerical examples.