Guaranteed cost controller for discrete time-delayed systems with actuator saturation

Abstract

The problem of guaranteed cost (GC) control using static-state feedback controllers for uncertain linear discrete time-delayed systems subjected to actuator saturation is studied in this paper. The stability analysis of closed-loop systems is carried out using a Lyapunov-Krasovskii functional. Conditions for the existence of state-feedback GC controllers are developed using a linear matrix inequality (LMI)-based criterion. The approach ensures a sufficient performance bound over all the acceptable parameter uncertainties. The scheme of the optimal GC controller problem is framed as a convex optimization problem with LMI constraints. The design of GC controllers for discrete-time systems subjected to actuator saturation without considering the effect of state-delay is also discussed. The effectiveness of the proposed approach is illustrated using suitable examples.

Optimal guaranteed cost control of discrete-time uncertain systems subjected to state saturation nonlinearity

“…Remark 2. The GC control problem for uncertain DT delayed systems with actuator saturation has been considered in Srivastava et al (2022). The effect of state saturation nonlinearities has not been considered in Srivastava et al (2022).…”

“…The GC control problem for uncertain DT delayed systems with actuator saturation has been considered in Srivastava et al (2022). The effect of state saturation nonlinearities has not been considered in Srivastava et al (2022). However, saturation overflow caused by finite word length constraint of digital technologies may lead to severe performance degradation and instability.…”

“…On the other hand, Theorem 1 makes use of the following sectorbased property of saturation nonlinearities: y T (t)Df(y(t))À f T (y(t))Df(y(t)) ø 0, where D is a positive-definite diagonal matrix. The result obtained in Theorem 1 is novel in the sense that such combination of parameter uncertainties and saturation nonlinearities for the study of GC problem for DT systems has not been investigated in earlier works (Arshad et al, 2016;Jungers and Daafouz, 2013;Massera et al, 2021;Srivastava et al, 2022;Zheng et al, 2022).…”

“…Using an attack-tolerant mechanism, an observer-based GC controller has been designed to assure exponential mean-square stability of the cyber-physical systems (Wang and Xu, 2019). The GC control method for DT delayed systems with actuator saturation has been proposed in Srivastava et al (2022). The strategy of GC control has been used in a variety of physical systems, such as networked control systems (Zheng et al, 2022), communication links (Chang et al, 2020), and cyber-physical systems (Wang and Xu, 2019).…”

“…Therefore, such approaches are not suitable for realizing GC controllers. On the other hand, the approaches in Arshad et al (2016), Chang et al (2020), Massera et al (2021), Srivastava et al (2022), and Zheng et al (2022) have not considered the effects of state saturation nonlinearities for the GC controller design. In the absence of parameter uncertainties, the GC control technique for DT systems employing state saturation has been investigated in Feng et al (2018).…”