A non-fragile observer-based adaptive sliding mode control for fractional-order Markovian jump systems with time delay and input nonlinearity

Abstract

In this paper, state estimation and adaptive sliding mode control (SMC) of uncertain fractional-order Markovian jump systems (FO-MJSs) with time delay and input nonlinearity are considered. A non-fragile observer is proposed to estimate the system states, and an observer-based adaptive sliding mode controller is synthesized to ensure the reachability of the sliding surfaces in the state-estimation space in finite time. The sufficient condition for stochastic stability of the error system and sliding mode dynamics is derived in the form of linear matrix inequalities (LMIs). Finally, some numerical examples are presented to illustrate the effectiveness of the proposed method.

Global Mittag-Leffler Synchronization of Fractional-Order Neural Networks With Time-Varying Delay via Hybrid Sliding Mode Control

“…Based on the SMC technique [40], [41], [42] and sampleddata feedback control approach [43], [44], [45], a hybrid or mixed SMC is designed to desire the GMLS for FNNTVD as follows…”

“…Compared with the controllers in [30], [31], [32], [33], [34], [35], [36], [37], SMC can deal with uncertainties and external disturbances more effectively [39]. Thereby, many scholars adopt SMC to study the dynamic performance of linear and nonlinear system [40], [41], [42]. For instance, in [40], a non-fragile observer-based adaptive SMC is designed to achieve stability for fractionalorder Markovian jump systems with time delay and input nonlinearity.…”

“…Thereby, many scholars adopt SMC to study the dynamic performance of linear and nonlinear system [40], [41], [42]. For instance, in [40], a non-fragile observer-based adaptive SMC is designed to achieve stability for fractionalorder Markovian jump systems with time delay and input nonlinearity. Furthermore, fixed-time synchronization problem of fractional-order memristive MAM neural networks is discussed by using SMC in [41].…”

“…From the previous works [40], [41], [42], two important aspects of SMC have not been considered yet, which are the influence of input time delay and how to reduce overconsumption of network resources. In practical applications, especially when communication speed and channels are limited, the input time delay is an unavoidable phenomenon, which may affect the input control performance, leading to the local oscillation or even the instability of whole system.…”

“…In practical applications, especially when communication speed and channels are limited, the input time delay is an unavoidable phenomenon, which may affect the input control performance, leading to the local oscillation or even the instability of whole system. In addition, in the previous works [40], [41], [42], since all the control schemes are the continuous-time feedbacks, they easily lead to the over-consumption system's resources and the channel congestion. In order to avoid these problems, recently sampled-data control, as a classical the discrete-time feedback control, is introduced [43], [44], [45].…”