Hybrid control for global stabilization of a class of systems (Q2758327)

The paper deals with the quadratic stability of switched systems. The article has two parts. In the first part a general description of hybrid systems and hybrid control is given. Three basic problems concerning stability of switched systems, which have been extensively studied in recent years, are enumerated: stability under switching laws, stability under certain classes of switching laws, and design of stabilizing switching laws. In the remainder of the first part, quadratic stability of homogeneous switched systems is studied. The author at first transforms the quadratic stability of systems into an equivalent restricted nonlinear programming problem and then gives a necessary and sufficient condition for quadratic stability with the Fritz John condition. NEWLINENEWLINENEWLINEIn the second part the author illustrates in detail how to design a hybrid controller for the cart-pendulum system. It is shown that the developed hybrid controller globally stabilizes the cart-pendulum system. It is declared that the method may be extended to other mechanical systems such as underactuated robot systems.NEWLINENEWLINEFor the entire collection see [Zbl 0968.00022].