Approximate “Controlled Lagrangian” stabilization of the furuta pendulum
Stabilization of mechanical control systems by the method of controlled Lagrangians in an approximate version, is used to analyze asymptotic stabilization of systems whose dynamics are governed by the Euler-Lagrange equations. The method is applied to the Furata pendulum. The approximation produces controlled near conservative stable orbits that can be asymptotically stabilized introducing dissipation.
In this paper, we study the almost periodic solutions for a class of Lasota-Wazewska models with patch structure on time scales. By using a fixed-point theorem and inequality techniques, some sufficient conditions are obtained which guarantee the existence and exponential stability of the almost periodic solutions. The criteria extend and improve some earlier results. Moreover, we give an examples to illustrate our main results.