Finite time stability and controller design for nonlinear impulsive sampled-data systems with applications

Exponential stabilization for nonlinear coupled dynamical systems via impulsive and sampled‐data control with input constraints

“…Remark It should be pointed out that some synchronization and stabilization criterion for neural networks with sampled‐data control and saturating actuators can also be considered in the works of Wu et al and Ding et al, but the effect of impulsive control on stabilization of neural networks has not been considered in the aforementioned works . It should be pointed out that some stabilization criterion for nonlinear impulsive systems with sampled‐data control can also be considered in the works of Lee et al and Lv and Li, but the effect of actuator saturation on stabilization of nonlinear impulsive systems has not been considered in the aforementioned works . Based on polytopic differential inclusion theorem, model can be described through a polytopic model.…”

“…18,19 It should be pointed out that some stabilization criterion for nonlinear impulsive systems with sampled-data control can also be considered in the works of Lee et al 25 and Lv and Li, 26 but the effect of actuator saturation on stabilization of nonlinear impulsive systems has not been considered in the aforementioned works. 25,26 Based on polytopic differential inclusion theorem, model (3) can be described through a polytopic model. The main advantage of this approach is that stability conditions can be obtained in a more tractable way, since the hard saturation nonlinearity disappear in the polytopic representation.…”

“…When the sampled‐data controller cannot guarantee the stability of the systems, the impulsive controller with constraints will be helpful for the stability of the systems. It should be pointed out that some synchronization and stabilization criterion for neural networks with sampled‐data control and saturating actuators can also be considered in the works of Wu et al and Ding et al, but the effect of impulsive control on stabilization of neural networks has not been considered in aforementioned works . In contrast to other works, the actuator saturation is taken into account in the design of the impulsive controller and the analysis of the stability of nonlinear coupled dynamical systems. Based on the established linear matrix inequalities (LMIs), we give the relatively least conservative conditions to ensure the local exponential stabilization of nonlinear coupled dynamical systems. A new sampled‐data and impulsive controller with partial input constraints is designed.…”

Analysis of Discontinuous Dynamical Behaviors of a Friction-Induced Oscillator with an Elliptic Control Law

“…In 2017, Fan et al [54] studied discontinuous dynamics of a friction-induced oscillator with switching control law of a straight line. For the examples of impulsive control and Boolean control as switching control law, see [55][56][57][58][59][60][61][62][63][64][65][66][67][68]. It is worth noting that the switching control law of an elliptic boundary has an important application in practical problem, such as satellite rendezvous and formation flight.…”

Finite-Time Stability of Uncertain Nonlinear Systems with Time-Varying Delay

“…The authors in [32] investigated the finite-time stability and designed a finite-time ∞ controller for a class of nonlinear time-delay Hamiltonian systems. Meanwhile, the finite-time stability or synchronization problem of neural networks was studied in [35][36][37][38][39][40][41][42]. It is worth noting that most of the results in literature focus on the finite-time stability for systems with or without time delays.…”