Preservation of exponential stability in discrete control systems with adaptive stabilization
Nonlinear, time-invariant, finite-dimensional closed-loop control systems are considered. It is assumed, that the controls are piecewise-constant functions with prescribed points of discontinuities. Under the additional assumptions on the smoothness of the functions in the differential state equations and algebraic output equations, sufficient conditions for preservation of exponential stability are formulated and proved. Adaptive stabilizability problems for linear time-invariant finite-dimensional dynamical systems with discrete controls are also considered. Moreover, remarks and comments on the relationships between different kinds of stability are given. Similar stability problems have been considered in the book of \textit{D. P. Derevitskij} and \textit{A. L. Fradkov} [Practical theory of discrete adaptive control systems (1981; Zbl 0518.93001) (in Russian)].
dynamical systems with discrete controls
scientific article; zbMATH DE number 4207944