Further Results on Quasi‐Synchronization of Delayed Chaotic Systems with Parameter Mismatches Via Intermittent Control

Abstract

This paper focuses on the problem of quasi-synchronization of delayed chaotic systems with parameter mismatches via aperiodically intermittent control. First, the intermittently controlled systems are modeled as switched systems with two modes. Then, piecewise switching-time-dependent Lyapunov functional/function are introduced for stability analysis of the switched systems. As a result, two novel sufficient conditions for quasi-synchronization are established under a small error bound. Based on the obtained quasi-synchronization criteria, the existence of the aperiodically intermittent controllers is presented in the form of Linear Matrix Inequalities (LMIs). Finally, chaotic neural networks and Chua's circuit are provided to verify the validity of the proposed method.

Exponential input‐to‐state stabilization of semilinear systems via intermittent control

“…$$ For any $$$ t>0 $$$, let $$$ {\tau}_1 $$$, $$$ {\tau}_2 $$$, $$$ \dots $$$, $$$ {\tau}_{N\left(t,0\right)} $$$ be the switching times on the interval $$$ \left(0,t\right) $$$ (by convention $$$ {\tau}_{N\left(t,0\right)+1}:= t $$$). Following, 36 consider the piecewise continuously differentiable function $$$$ W(s)={\mathrm{e}}^{\delta s}V(s). $$$$ From (21), (23) and (24), we obtain $$$$ \dot{W}(s)\le {\mathrm{e}}^{\delta s}\gamma {\left|v(s)\right|}^2,\kern0.60em s\in \left[{\tau}_i,{\tau}_{i+1}\right), $$$$ where …”