3,854 research outputs found
On feedback stabilization of linear switched systems via switching signal control
Motivated by recent applications in control theory, we study the feedback
stabilizability of switched systems, where one is allowed to chose the
switching signal as a function of in order to stabilize the system. We
propose new algorithms and analyze several mathematical features of the problem
which were unnoticed up to now, to our knowledge. We prove complexity results,
(in-)equivalence between various notions of stabilizability, existence of
Lyapunov functions, and provide a case study for a paradigmatic example
introduced by Stanford and Urbano.Comment: 19 pages, 3 figure
Continuous Uniform Finite Time Stabilization of Planar Controllable Systems
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 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
Stability of Planar Nonlinear Switched Systems
We consider the time-dependent nonlinear system , where , and are two
% smooth vector fields, globally asymptotically stable at the origin
and is an arbitrary measurable function. Analysing the
topology of the set where and are parallel, we give some sufficient and
some necessary conditions for global asymptotic stability, uniform with respect
to . Such conditions can be verified without any integration or
construction of a Lyapunov function, and they are robust under small
perturbations of the vector fields
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