Quantized <italic>l</italic>&#x2082;-<italic>l</italic>&#x221E; Control for Nonlinear Discrete-Time Systems With DoS Attacks

Abstract

The quantitative control problem of nonlinear discrete-time systems under DoS attacks is studied in this paper. The nonlinear part of the system is approximated linearly by T-S fuzzy model. Unknown DoS attacks are defined and modeled in terms of attack frequency and attack duration. By adding dynamic system, an intermediate observer is designed to estimate the system states. Dynamic quantizers and controllers are used to quantify and control system signals in different modes, a descriptor representation form of mode-dependent closed-loop control system can be constructed. By defining the mode-dependent Lyapunov function, the design conditions of quantizers and controllers can be obtained to satisfy the system mean-square exponential stability and the desired $l_{2}-l_{\infty }$ performance. Finally, a nonlinear mass-spring-damper mechanical system is used to verify the effectiveness of the method.

Keywords

• DoS attacks
• intermediate observer
• dynamic quantization
• mode-dependent Lyapunov function