Synchronization Control Design Based on Wirtinger Inequality for Uncertain Coronary Artery Time-Delay System With Input Saturation

Abstract

This paper focuses on the synchronization of uncertain coronary artery chaos systems (CACSs) with the state and input time-varying delays under input saturation. First, the stability of the closed-loop system is established to ensure the synchronization between the diseased and healthy CACSs under input saturation by utilizing the local sector condition and the Lyapunov-Krasovskii functional (LKF) method. The use of Wirtinger inequality and the reciprocally convex method further reduces the conservatism. Second, by making use of the cone complementary linearization approach to deal with nonlinear terms, we obtained a state feedback controller. Finally, a robust state feedback controller is formulated to achieve the synchronization of the CACS under disturbances bounded by L 2 norm. The simulation results of the CACS synchronization are presented to demonstrate the effectiveness of the derived results, which provides a certain theoretical basis for curing diseases related to the coronary artery vessel.

Finite-time H∞ synchronization control for coronary artery chaos system with input and state time-varying delays

“…The simulations show that our synchronization strategy effectively synchronizes the convulsive coronary system with the healthy cardiovascular system under input delay and disturbance. In future work, the results and methods in this work are expected to use to other various systems in real-word application, for instant, H 1 control [6][7][8][9], mixed H 1 and passive performance index [10], adaptive control [11,12], fuzzy control [13], observer-based control [14,15] and state-feedback control [16], projective synchronization of chaotic systems [43] and stochastic differential equations [44]. Furthermore, input delay and state delay will be considered in different values to get more closer to reality.…”

“…Definition 2 [8] Under zero initial conditions, the error system (7) is based on the H 1 performance index.…”

“…Therefore, the integrity of the system is critical. Several effective methods are used to achieve the synchronization between the healthy CACS and diseased CACS such as H 1 control [6][7][8][9], mixed H 1 and passive performance index [10], adaptive control [11,12], fuzzy control [13], observerbased control [14,15] and state-feedback control [16]. Particularly, Zhang et al [6] studied problems of the synchronization CACS with input disturbances and input time-delay depending on H 1 control.…”

“…Li et al [7] investigated H 1 control for CACS via free-matrix-based integral inequality with time-delay. The authors in [8] studied uncertain CACS of synchronization controller design depending on Wirtinger integral inequality with input saturation and time delay. The authors in [9] considered the CACS for H 1 synchronization problems with input time-varying delay and input disturbances.…”