4,610 research outputs found
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
Transverse Contraction Criteria for Existence, Stability, and Robustness of a Limit Cycle
This paper derives a differential contraction condition for the existence of
an orbitally-stable limit cycle in an autonomous system. This transverse
contraction condition can be represented as a pointwise linear matrix
inequality (LMI), thus allowing convex optimization tools such as
sum-of-squares programming to be used to search for certificates of the
existence of a stable limit cycle. Many desirable properties of contracting
dynamics are extended to this context, including preservation of contraction
under a broad class of interconnections. In addition, by introducing the
concepts of differential dissipativity and transverse differential
dissipativity, contraction and transverse contraction can be established for
large scale systems via LMI conditions on component subsystems.Comment: 6 pages, 1 figure. Conference submissio
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