About state estimation of logical-dynamic system with delay

D.Ya.Khusainov, O.I.Kuzmych

National University of Kiev

Vladimirskaya Str., 64, 01033, Kiev, Ukraine

J.Diblík

Žilina University, Faculty of Science

J. M. Hurbana, 15, Žilina 01026, Slovak Republic

 

Recent problems arising in many science fields are often mathematically modeled as dynamic systems having various structures. Frequently, hybrid or logical-dynamical systems are used as adequate mathematical models. One of the latest research problem is the investigation of perturbations in hybrid systems of dynamic systems. In various branches of science such as engineering, economy, ecology or design of control systems, more adequate instruments for mathematical modeling and investigation of such systems are hybrid systems defined, e.g., as a set of subsystems of discrete equations with delay. In the paper, we investigate dynamical hybrid systems in the form of the union of a set of linear difference subsystems with constant coefficients and constant delays. We derive an estimate of perturbations of such systems. We consider two main cases: the case of stable subsystems and the case of unstable subsystems. The investigation is performed via the Lyapunov-Krasovsky functional method.

systems.