Stabilization of observable linear system of control with constant interval coefficients
In the paper linear, continuous-time, finite-dimensional control systems with constant coefficients with values from given closed intervals are considered. First, controllability and observability concepts are recalled. Next, using methods taken from mathematical analysis and predictive control, a stabilizing feedback linear control is proposed and discussed. Moreover, taking into account the form of the controllability and observability matrices, estimations of phase states are proposed. Finally, sufficient conditions for the stabilization property are formulated and proved. The paper contains also many remarks and comments on the stabilization problem for linear control systems. Moreover, it should be pointed out that similar problems have been considered in the monographs [\textit{E. B. Lee} and \textit{L. Markus}, Foundations of optimal control theory (The SIAM Series in Applied Mathematics) New York: John Wiley and Sons (1967; Zbl 0159.13201) and \textit{J. Klamka}, Controllability of dynamical systems (Mathematics and Its Applications: East European Series 48) Dordrecht: Kluwer Academic Publishers (1991; Zbl 0732.93008)]. The results given in the paper can be extended to discrete-time linear systems with constant coefficients and a discrete state equation.
scientific article; zbMATH DE number 1960448