Asymptotic controllability and observability imply semiglobal practical asymptotic stabilizability by sampled-data output feedback

Authors:
H. Shim;A. R. Teel
Affiliations:
Division of Electrical and Computer Engineering, Hanyang University, Haengdang 17, Seoul, 133-791, South Korea;CCEC, Electrical and Computer Engineering Department, University of California, Santa Barbara, CA 93106-9560, USA
Venue:
Automatica (Journal of IFAC)
Year:
2003

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Abstract

It is shown, for general nonlinear systems, that asymptotic controllability and observability are sufficient for semiglobal practical asymptotic stabilization by output feedback. Indeed, as previously shown in the literature, asymptotic controllability implies the existence of a (discontinuous in general) state feedback that, when implemented by sample and hold, is semiglobally practically stabilizing and robust to measurement disturbance; moreover, a weak form of observability allows reconstruction of the state with arbitrary precision in an arbitrarily short amount of time. So, we can build an output feedback that operates periodically in two modes: an initial, small fraction of a sampling period is used to estimate the state, and the remainder of the sampling period is used to implement the state feedback control using the state estimate. Our stabilization results are presented not only for compact target sets (e.g., the origin) but also for noncompact target sets.