DocumentCode :
3608480
Title :
Regional observer synthesis for locally Lipschitz non-linear systems
Author :
Rehan, Muhammad ; Keum-Shik Hong
Author_Institution :
Dept. of Electr. Eng., Pakistan Inst. of Eng. & Appl. Sci., Islamabad, Pakistan
Volume :
9
Issue :
16
fYear :
2015
Firstpage :
2348
Lastpage :
2356
Abstract :
This study discusses a linear matrix inequality (LMI)-based observer design for locally Lipschitz non-linear systems that ensures an ellipsoidal region of stability in the estimation error, via a quadratic Lyapunov function analysis. An ellipsoidal Lipschitz region is defined in which a dynamical non-linearity satisfies the Lipschitz condition locally. First, to provide a state feedback stabilisation scheme, the region of stability in terms of state of a non-linear system is included in the ellipsoidal Lipschitz region, and LMIs are derived to ensure asymptotic stability. This novel state feedback stabilisation technique is broadened to the observer synthesis by defining a new region in the form of state estimation error, satisfying the ellipsoidal Lipschitz region. Further, under a bounded state operation, the region of convergence is included in the new region. Furthermore, a local robust observer synthesis methodology against bounded perturbations, for attaining multiple design objectives, is provided by ensuring the local exponential L2 stability of the estimation error. The proposed methodologies´ guaranteed regional stability, faster convergence, robustness against disturbances, ease of design, and computational simplicity make them superior from the traditional techniques. The results for the proposed schemes are validated by numerical simulations.
Keywords :
Lyapunov methods; asymptotic stability; control nonlinearities; control system synthesis; linear matrix inequalities; nonlinear control systems; observers; state feedback; LMI; dynamical nonlinearity; ellipsoidal Lipschitz region; ellipsoidal stability region; linear matrix inequality-based observer design; local exponential L2 stability; local robust observer synthesis methodology; locally Lipschitz nonlinear systems; multiple design objectives; numerical simulations; quadratic Lyapunov function analysis; regional observer synthesis; stabilisation controller design; state estimation error; state feedback stabilisation scheme;
fLanguage :
English
Journal_Title :
Control Theory Applications, IET
Publisher :
iet
ISSN :
1751-8644
Type :
jour
DOI :
10.1049/iet-cta.2015.0315
Filename :
7299712
Link To Document :
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