Dichotomy property and Lagrange stability for uncertain pendulum-like feedback systems

In this note, property of dichotomy and Lagrange stability of the uncertain pendulum-like systems with additional, multiplicative and H∞H∞ uncertainty are considered, respectively. By using some results of H∞H∞ theory the property of dichotomy and Lagrange stability of uncertain pendulum-like systems with multiple equilibria are transformed into L∞L∞ or H∞H∞ norm condition of some transfer functions. The convergence problem of all bounded solutions for some uncertain pendulum-like systems can be converted into the internal stability of another system under unstructured perturbations.