Input-to-state stabilization of the perturbed systems in the generalized triangular form

2010/08/27 by Sergey Dashkovskiy, Dashkovskiy, Sergey, Svyatoslav S. Pavlichkov +2
Computer Science · Engineering · Mathematics · #Advanced Differential Equations and Dynamical Systems #Aerospace Engineering and Control Systems #Cybersecurity and Information Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Optimization and Control (math.OC) #math.DS #math.OC

paper · pdf · doi:10.48550/arxiv.1008.4674

19 pages

arxiv created 2010/08/27 · openalex publication_date 2010/08/27 · arxiv updated 2010/08/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We consider nonlinear control systems of the so-called generalized triangular form (GTF) with time-varying and periodic dynamics which linearly depends on some external disturbances. Our purpose is to construct a feedback controller which provides the global input-to-state stability of the corresponding closed-loop w.r.t. the disturbances. To do this, we combine the method proposed in the earlier work \citepavlichkov_ge₂009 devoted the the global asymptotic stabilization of the GTF systems without disturbances with the ISS theory for time-varying systems proposed in \citewang. Following this pattern we construct a feedback which provides the properties of uniform global stability and asymptotic gain w.r.t the disturbances. Then we obtain the semi-uniform ISS of the closed-loop system.

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