On stabilization of nonlinear systems with enlarged domain of attraction

✍ Scribed by K. Ichikawa; R. Ortega

• Publisher: Elsevier Science
• Year: 1992
• Tongue: English
• Weight: 330 KB
• Volume: 28
• Category: Article
• ISSN: 0005-1098
• DOI: 10.1016/0005-1098(92)90188-l

✦ Synopsis

This paper presents a systematic procedure to design a control law that guarantees asymptotic stability of an equilibrium with an enlarged domain of attraction for a class of nonlinear systems. To this end, we use a natural extension of well-known linear time-invariant transformation methods to write the system in controller canonical form with a forcing term. The control law is implemented in two steps, first we calculate a nonlinear state feedback that cancels the nonlinear terms of the unforced system, so that for the resulting system a suitable Lyapunov function candidate is available. Then, we add a linear state feedback that stabilizes the equilibrium and maximizes its domain of attraction. Interestingly enough, the latter maximization problem reduces to a classical, linear time invariant H® minimization problem. An example is given to illustrate the procedure.