Synchronization of A Class of Uncertain Chaotic Systems with Lipschitz Nonlinearities Using State‐Feedback Control Design: A Matrix Inequality Approach

Abstract

This paper proposes a new state-feedback stabilization control technique for a class of uncertain chaotic systems with Lipschitz nonlinearity conditions. Based on Lyapunov stabilization theory and the linear matrix inequality (LMI) scheme, a new sufficient condition formulated in the form of LMIs is created for the chaos synchronization of chaotic systems with parametric uncertainties and external disturbances on the slave system. Using Barbalat's lemma, the suggested approach guarantees that the slave system synchronizes to the master system at an asymptotical convergence rate. Meanwhile, a criterion to find the proper feedback gain vector F is also provided. A new continuous-bounded nonlinear function is introduced to cope with the disturbances and uncertainties and obtain a desired control performance, i.e. small steady-state error and fast settling time. Several criteria are derived to guarantee the asymptotic and robust stability of the uncertain master-slave systems. Furthermore, the proposed controller is independent of the order of the system's model. Numerical simulation results are displayed with an expected satisfactory performance compared to the available methods.

Analysis and control of spatial limit sets and spatial chaos appearance in mimo cascade connected nonlinear systems

“…Each cascade is described with a set of equations: cascade connected nonlinear system (22), Fig. 10a, becomes stable focus, Fig.…”

“…10d. Figs 11a and 11b show the strange attractor and parametric curve of cascade system (22) for l 3 = 0.6, respectively. Fig.…”

“…These values are located in the interval [-1, 2.9035]. After applying the modified Pyragas method (17), for K = 0.5, spatial chaos of MIMO cascade connected nonlinear system (22), in Fig. 11a, becomes stable focus, Fig.…”

“…It can be noted for system (22) that the limit sets degenerate if the trajectory l intersects the peripheral part of region S 3 , which is expected. The more the trajectory l approaches the peripheral part of region S 3 , the more motion (22) for l 3 = 0.37 after applying the modified Pyragas method (17) for K = 0.5. becomes chaotic and limit sets get a fractal structure. Finally, if l would not intersect the region S 3 , there would be no limit sets at all.…”

Controlling Chaos and Neimark–Sacker Bifurcation in a Host–Parasitoid Model

“…Recently, in [1,23,24,32,33,35], the parametric conditions for existence and direction of Neimark-Sacker bifurcation are investigated, and in [1,32,33,35] feedback chaos control strategies are implemented for controlling chaos and bifurcations in host-parasitoid models. Moreover, for state-feedback control design based on the matrix inequality approaches, we refer to [63][64][65][66].…”