Continuous Uniform Finite Time Stabilization of Planar Controllable Systems
Continuous Uniform Finite Time Stabilization of Planar Controllable Systems
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DOI：
10.1137/120877155
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发表时间：
2015-05
期刊：
影响因子：
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通讯作者：
Harshal B. Oza;Y. Orlov;S. Spurgeon
中科院分区：
文献类型：
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作者：
Harshal B. Oza;Y. Orlov;S. Spurgeon
连续齐次控制器用于全状态反馈设置，以在存在均匀衰减分段连续扰动的情况下实现扰动双积分器的均匀有限时间稳定性。确定半全局强 $\mathcal{C}^1$ Lyapunov 函数以建立闭环平面系统的一致渐近稳定性。然后，通过将不连续系统的齐次性原理扩展到具有均匀衰减的分段连续非齐次扰动的连续情况，证明了均匀有限时间稳定性。还计算了稳定时间的有限上限。结果通过提出均匀有限时间稳定性和处理平面可控系统更广泛的非齐次扰动，同时还提出了一类新型齐次连续控制器，扩展了关于齐次性和有限时间稳定性的现有文献。
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.