Controllability of impulsive second-order nonlinear systems with nonlocal conditions in Banach spaces

Abstract

In this paper, we are concerned with the controllability of damped second-order integrodifferential systems with impulses. Further the result is extended to study the controllability of nonlinear neutral systems with nonlocal conditions. The fixed point analysis approach is adopted in investigation. Sufficient conditions are formulated with a noncompact condition on the cosine family of operators. The results are obtained using the Banach fixed point theorem. An example is presented to illustrate the results.

Robust adaptive passivity‐based control of open‐loop unstable affine non‐linear systems subject to actuator saturation

“…Consider the following disturbed system: where represents the disturbance. It is noteworthy that although the disturbance is assumed to be bounded, it can cause abrupt changes in the state variables of the system [37]. Here, the projection method is used to prevent parameter drift, which needs some a priori knowledge about the true system parameters.…”

Archives of Control Sciences

“…To mention some of them, we have the work done by Leiva about the controllability of semilinear impulsive nonautonomous systems by the use of Rothe's fixed point theorem [6]. The work done by Balachandran and Arthi about the controllability of nonlinear system with impulses and nonlocal conditions using Banach fixed point theorem [7], as well as the work done by Selvi and Malik about the controllability of impulsive differential systems with finite delay by using measures of noncompactness and Monch fixed point theorem [8]. And recently, the work done by Malik et al about the controllability of a non-autonomous nonlinear differential system with non-instantaneous impulses [9].…”