Non-fragile – control for discrete-time stochastic nonlinear systems under event-triggered protocols

Abstract

In this paper, the non-fragile ${\ell }_2$–${\ell }_{\infty }$ control problem is investigated for a class of discrete-time stochastic nonlinear systems under event-triggered communication protocols, which determine whether the measurement output should be transmitted to the controller or not. The main purpose of the addressed problem is to design an event-based output feedback controller subject to gain variations guaranteeing the prescribed disturbance attenuation level described by the ${\ell }_2$–${\ell }_{\infty }$ performance index. By utilizing the Lyapunov stability theory combined with S-procedure, a sufficient condition is established to guarantee both the exponential mean-square stability and the ${\ell }_2$–${\ell }_{\infty }$ performance for the closed-loop system. In addition, with the help of the orthogonal decomposition, the desired controller parameter is obtained in terms of the solution to certain linear matrix inequalities. Finally, a simulation example is exploited to demonstrate the effectiveness of the proposed event-based controller design scheme.

Keywords:

• ${\ell }_2$–${\ell }_{\infty }$ control
• event-triggered protocol
• non-fragile control
• stochastic nonlinearities

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China [grant number 61573246], [grant number 61603255] and [grant number 61503001]; the Shanghai Rising-Star Program of China [grant number 16QA1403000]; the Program for Capability Construction of Shanghai Provincial Universities [grant number 15550502500]; and the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning.