Φ0-stability of Impulsive Hybrid Setvalued Differential Equations with Delay by Perturbing Lyapunov Functions

The study of set differential equations has been initiated as an independent subject and several results of interest can be found in [4–5, 10–12, 14]. The interesting feature of the set differential equations is that the results obtained in this new framework become the corresponding results of ordinary differential equations as the Hukuhara derivative and the integral used in formulating the set differential equations reduce to the ordinary vector derivative and integral when the set under consideration is a single valued mapping. Moreover, in the present setup, we have only semilinear complete metric space to work with, instead of complete normed linear space required in the study of the ordinary differential systems. Furthermore, set differential equations, that are generated by multivalued differential inclusions, when the multivalued functions involved do not possess convex values, can be used as a tool for studying multivalued differential inclusions [20]. Set differential equations can also be utilized to investigate fuzzy differential equations [11]. In recent years, a number of research papers has dealt with dynamical systems with impulse effect as a class of general hybrid systems. Examples include the adequate mathematical models for numerous processes and phenomena studied in biology, applied physics, etc. Impulsive dynamical systems are characterized by the