# Continuous Uniform Finite Time Stabilization of Planar Controllable Systems

Oza, Harshal B., Orlov, Yury V., Spurgeon, Sarah K. (2015) Continuous Uniform Finite Time Stabilization of Planar Controllable Systems. SIAM Journal on Control and Optimization, 53 (3). pp. 1154-1181. ISSN 0363-0129. (doi:10.1137/120877155)

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http://doi.org/10.1137/120877155

## Abstract

Continuous homogeneous controllers are utilized in a full state feedback setting for the uniform finite time stabilization of a perturbed double integrator in the presence of uniformly decaying piecewise continuous disturbances. Semiglobal strong $\mathcal{C}^1$ Lyapunov functions are identified to establish uniform asymptotic stability of the closed-loop planar system. Uniform finite time stability is then proved by extending the homogeneity principle of discontinuous systems to the continuous case with uniformly decaying piecewise continuous nonhomogeneous disturbances. A finite upper bound on the settling time is also computed. The results extend the existing literature on homogeneity and finite time stability by both presenting uniform finite time stabilization and dealing with a broader class of nonhomogeneous disturbances for planar controllable systems while also proposing a new class of homogeneous continuous controllers.

Item Type: Article 10.1137/120877155 T Technology Faculties > Sciences > School of Engineering and Digital ArtsFaculties > Sciences > School of Engineering and Digital Arts > Instrumentation, Control and Embedded Systems Tina Thompson 26 May 2015 08:16 UTC 29 May 2019 14:36 UTC https://kar.kent.ac.uk/id/eprint/48646 (The current URI for this page, for reference purposes)