Abstract
Abstract. The aim of this paper is to study the controllability and ob-servability for a class of linear time-varying impulsive control systems on timescales. Sufficient and necessary conditions for state controllability and stateobservability of such systems are established. The corresponding criteria fortime-invariant impulsive control systems on time scales are also obtained.Keywords: time scale, linear impulsive control system, controllability,observability.AMS Subject Classification: 93B05, 34A37, 34H05, 93B07. 1 Introduction Differential equations with impulses have a considerable importance in variedapplications as physics, engineering, biology, medicine, economics, neuronalnetworks, social sciences, and so on. Many investigations have been car-ried out concerning the existence, uniqueness, and asymptotic properties ofsolutions. We refer to the monographs [7, 11, 29, 40] and the referencestherein. It is well known that the study of controllability plays an importantrole in the control theory. In recent years, some research dealing with thestudy of controllability for impulsive systems [10, 16, 23, 32, 34, 41, 44, 47].The most dynamical systems are analyzed in either the continuous or dis-crete time domain. The population dynamical models in continuous timeare usually appropriate for organism that have overlapping generations. Onother hand, many biological populations are more accurately described bynon-overlapping generations. The dynamics of these populations often are
Highlights
Differential equations with impulses have a considerable importance in varied applications as physics, engineering, biology, medicine, economics, neuronal networks, social sciences, and so on
Some research dealing with the study of controllability for impulsive systems [10, 16, 23, 32, 34, 41, 44, 47]
The population dynamical models in continuous time are usually appropriate for organism that have overlapping generations
Summary
Differential equations with impulses have a considerable importance in varied applications as physics, engineering, biology, medicine, economics, neuronal networks, social sciences, and so on. The most dynamical systems are analyzed in either the continuous or discrete time domain. The population dynamical models in continuous time are usually appropriate for organism that have overlapping generations. A such sequential-continuous model can be formulated by the help of dynamical systems on time scales. There has been significant growth in the theory of dynamic systems on time scales, covering a variety of different qualitative aspects. Some authors studied impulsive dynamic systems on time scales [4, 11, 12, 26, 31, 33, 35]. The main purpose of this paper is to derive necessary and sufficient criteria for controllability and observability of a class of such systems on time scales
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