Input to State Stabilizability for Parametrized Families of Systems
نویسندگان
چکیده
This paper studies various stability issues for parametrized families of systems, including problems of stabilization with respect to sets. The study of such families is motivated by robust control applications. A Lyapunov-theoretic necessary and sufficient characterization is obtained for a natural notion of robust uniform set stability; this characterization allows replacing ad hoc conditions found in the literature by more conceptual stability notions. We then use these techniques to establish a result linking state-space stability to ‘input to state’ (bounded-input bounded-state) stability. In addition, the preservation of stabilizability under certain types of cascade interconnections is analysed.
منابع مشابه
Input to State Stabilizability for Parameterized Families of Systems
This paper studies various stability issues for parameterized families of systems, including problems of stabilization with respect to sets. The study of such families is motivated by robust control applications. A Lyapunov-theoretic necessary and sufficient characterization is obtained for a natural notion of robust uniform set stability; this characterization allows replacing ad hoc condition...
متن کاملRational representations of behaviors : well - posedness , stability and stabilizability
This paper presents an analysis of representation and stability properties of dynamical systems whose signals are assumed to be square summable sequences. Systems are understood as families of trajectories with no more structure than linearity and shift-invariance. We depart from the usual input-output and operator theoretic setting and view relationships among system variables as a more genera...
متن کاملInput – Output Stabilization of Linear Systems on
A formal framework is set up for the discussion of generalized autoregressive with external input models of the form = , where and are linear operators, with the main emphasis being on signal spaces consisting of bounded sequences parametrized by the integers. Different notions of stability are explored, and topological notions such as the idea of a closed system are linked with questions of st...
متن کاملNonlinear stabilizability via encoded feedback: The case of integral ISS systems
In this note we observe how, using the same arguments of Liberzon and Hespanha [(2005). Stabilization of nonlinear systems with limited information feedback, IEEE Transactions on Automatic Control, 50, 910–915] , integral input-to-state stabilizability with respect to measurement errors is enough to prove stabilizability of nonlinear systems with limited information. The utility of the remark l...
متن کاملReport SYCON-88-15 FURTHER FACTS ABOUT INPUT TO STATE STABILIZATION
Previous results about input to state stabilizability are shown to hold even for systems which are not linear in controls, provided that a more general type of feedback be allowed. Applications to certain stabilization problems and coprime factorizations, as well as comparisons to other results on input to state stability, are also brieey discussed.
متن کامل