Open AccessInput‐to‐state stability of an ODE‐heat cascade system with disturbances
Author(s) -
Zhang YuLong,
Wang JunMin,
Guo YaPing
Publication year - 2019
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2018.5816
Subject(s) - control theory (sociology) , ode , cascade , backstepping , mathematics , ordinary differential equation , stability (learning theory) , exponential stability , observer (physics) , interconnection , boundary (topology) , state observer , differential equation , computer science , nonlinear system , control (management) , engineering , adaptive control , mathematical analysis , physics , artificial intelligence , chemical engineering , machine learning , computer network , quantum mechanics
In this study, the authors consider the input‐to‐state stability of an ordinary differential equation (ODE)–heat cascade system with Dirichlet interconnection where the boundary control input is located at the right end of the heat equation and the disturbance is appeared as a non‐homogeneous term in the ODE. Based on two backstepping transformations, they design a state feedback control law that guarantees the input‐to‐state stability of the closed‐loop system. The well‐posedness of the closed‐loop system is presented by using the semi‐group approach. Moreover, they design an output feedback control law by constructing an exponentially convergent observer. With the output feedback control, the input‐to‐state stability of the resulting closed‐loop system is proven.