Stability of nonlinear systems with variable-time impulses: B-equivalence method

Coordinated Tracking for Nonlinear Multiagent Systems under Variable‐Time Impulsive Control

“…We have the observations that if H1 holds, for ( < < ), ∈ Z + , then each solution ( ) of (10) intersects Γ and Γ must intersect Γ and intersect every surface Γ ; if H2 and H3 hold, each solution ( ) of (10) intersects Γ at most once. This proof follows theorem 1 in [16]; we omit it. Now we shall use B-equivalent method to construct the comparison system of system (10).…”

“…By using this method, variable-time impulsive system can be reduced to fixed-time one, which can be regarded as the comparison system of the original one. Based on these results, a theoretical framework was formulated to reveal the principle of reduction and comparison in nonlinear variable-time impulsive system in [16]. The authors therein constructed the relationship between the original jump operator and comparison system jump operator and then demonstrated that the two systems have the same stability property.…”

“…Coordinated tracking criteria of variabletime impulsive controller can be derived by analyzing fixedtime impulsive one without any difficulty. Second, from the variable-time impulsive system [16][17][18][19][20][21] standpoint, we extend the application of B-equivalence method on one dynamic to multiple dynamics, which should consider the constrains of communication topology among dynamics. And, moreover, coordinated tracking controller is designed to specific function containing impulsive matrices; this is more challenging in analysis than virtual functions in [16][17][18][19][20][21].…”

State-dependent Impulsive Control for Consensus of Multi-agent Systems

“…Akhmet introduced and developed B-equivalence method to reduce a system with variable-time impulsive instants to a fixed-time impulsive system [30,31]. Along this line, Li and his colleagues formulated a throughout theoretical framework of reduction and comparison principle for variable-time impulsive control in nonlinear systems [32]. They firstly formulated the relationship between original jump operator and corresponding new ones.…”

Time-delayed impulsive control for discrete-time nonlinear systems with actuator saturation

“…However, the control problem for difference dynamic system via delayed impulsive control with actuator saturation has not been fully investigated yet, and many challenging questions remain. So far, there have been many studies on impulsive control, but the impulses are basically unconstrained [1,13,16,32,35,36,38]. Based on this, this paper proposes a special type of delayed-impulse controller with actuator saturation, the controller of which engages the feedback control laws and analyzes the exponentially stability of the closed loop.…”