Robust output feedback stabilization via a small gain theorem

✍ Scribed by S. Battilotti

• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 299 KB
• Volume: 8
• Category: Article
• ISSN: 1049-8923
• DOI: 10.1002/(sici)1099-1239(199803)8:3<211::aid-rnc256>3.0.co;2-9

✦ Synopsis

In this paper, we give sufficient conditions for designing robust globally stabilizing controllers for a class of uncertain systems, consisting of 'nominal' nonlinear minimum phase systems perturbed by uncertainties which may affect the equilibrium point of the nominal system ('biased' systems). The constructive proof combines a systematic step-by-step procedure, based on H arguments, with a small gain theorem, recently proved for nonliner systems. At each step, one finds two Lyapunov functions, one for a state-feedback problem and the other one for an output injection problem. Combining these two functions, one derives at each step a Lyapunov function candidate for solving an ouptut feedback stabilization problem. This approach allows one to put into a unified framework many existing results on robust output feedback stabilization.