We consider the simplest design problem for nonlinear systems: the problem of rendering asymptotically stable a given equilibrium by means of feedback. For such a problem, we provide a necessary condition, known as Brockett condition, and a sufficient condition, which relies upon the definition of a class of functions, known as control Lyapunov functions. The theory is illustrated by means of a few examples. In addition we discuss a nonlinear enhancement of the so-called separation principle for stabilization by means of partial state information.
Astolfi, A. (2021). Feedback Stabilization of Nonlinear Systems. In T.S. John Baillieul (a cura di), Encyclopedia of Systems and Control (pp. 794-803). Springer [10.1007/978-3-030-44184-5_85].
Feedback Stabilization of Nonlinear Systems
Astolfi, Alessandro
2021-08-01
Abstract
We consider the simplest design problem for nonlinear systems: the problem of rendering asymptotically stable a given equilibrium by means of feedback. For such a problem, we provide a necessary condition, known as Brockett condition, and a sufficient condition, which relies upon the definition of a class of functions, known as control Lyapunov functions. The theory is illustrated by means of a few examples. In addition we discuss a nonlinear enhancement of the so-called separation principle for stabilization by means of partial state information.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
