Robust control for a class of uncertain neutral‐type systems with time‐varying delays

Abstract

This paper investigates the problem of robust H∞ asymptotic stabilization for a class of uncertain neutral‐type systems with time‐varying delays. A sufficient condition is obtained to ensure the considered system is robust asymptotic stabilization with disturbance attenuation level γ, which is based on the sliding mode observer framework. Meanwhile, a novel integral sliding surface function with the compensator is proposed to make sure the considered system can be stabilized. And the gain matrix is obtained by solving a strict linear matrix inequality. Finally, two numerical examples are provided to demonstrate the validity and potential of the proposed method.

Sliding mode projective synchronization for fractional-order coupled systems based on network without strong connectedness

“…Since proposed by Emelyanov in the 1960s (Emelyanov, 1967), sliding mode control (SMC) has been used in neutral-type systems (Meng et al, 2020), singular systems (Liu et al, 2017), Markovian jump systems (Karimi, 2012), uncertain stochastic systems (Liu et al, 2020) and other practical engineering systems (Su et al, 1992) due to its fast response, good transient performance and other features. For example, Liu M et al (2018) investigated the problem of fault estimation sliding-mode observer design for linear systems over digital communication channels.…”

Further results on delay-dependent robust H∞ control for uncertain systems with interval time-varying delays

“…It is well recognized that the existence of delays and uncertainty often causes poor performance, oscillation or even system instabilities (Qian et al, 2017;Wang et al, 2017). Therefore, the stability analysis of uncertain systems with time-varying delays has become an important issue in theory and application, and many related problems also have been researched, such as robust stability (Cheng et al, 2016;Li & Liao, 2018;Lu et al, 2019), H ∞ performance (Ding et al, 2017;Kwon et al, 2016;Meng et al, 2020), passivity (Peng & Jian, 2018), control (Niamsup & Phat, 2020). During the past decades, lots of fruitful results have been achieved.…”

“…to estimate the derivative of LKF more accurately, such as delay partitioning approach (Ding et al, 2017), freematrix-based integral inequality (Wang et al, 2017), the augmented LKF approach (Meng et al, 2020;Peng & Jian, 2018), Wirtinger-based inequality (Li & Liao, 2018), reciprocally convex combination (Kwon et al, 2016;Li & Xue, 2016;Zhang et al, 2017), auxiliary function-based integral inequality (Zhang et al, 2018) and Bessel-Legendre inequality (Seuret & Gouaisbaut, 2018). Recently, considering the disturbances and parameter uncertainty in modelling, the robust H ∞ control has been studied in Bai et al (2016), Sun et al (2018), Meng et al (2020) and Niamsup and Phat (2020). In Meng et al (2020), based on the sliding mode observer framework, a sufficient condition and novel integral sliding surface function with the compensator were proposed to investigate robust H ∞ asymptotic stabilization for uncertain neutral-type systems.…”

“…Recently, considering the disturbances and parameter uncertainty in modelling, the robust H ∞ control has been studied in Bai et al (2016), Sun et al (2018), Meng et al (2020) and Niamsup and Phat (2020). In Meng et al (2020), based on the sliding mode observer framework, a sufficient condition and novel integral sliding surface function with the compensator were proposed to investigate robust H ∞ asymptotic stabilization for uncertain neutral-type systems. A new delay-dependent sufficient condition for admissibility of the system with nondifferentiable delay was presented, and state feedback controllers was designed which ensure the descriptor closed-loop system admissible with a maximum H ∞ disturbance attenuation level in Niamsup and Phat (2020).…”

Observer-based SMC for stochastic systems with disturbance driven by fractional Brownian motion

“…As we know, sliding mode control (SMC) [22,17,27] plays an important role in theoretical research and engineering technology for complex systems, such as in the field of automotive control systems [27], UAV swarm motion [13], secure communications [3], amplifier circuit systems [21], fractional-order systems [18], semi-Markovian jump systems [6], neural networks [25] and observer design [7,23,15], etc. In [25], Yan et al investigated stochastic exponential stability problems for switched neural networks.…”