Adaptive sliding mode observer design for a class of uncertain systems

Abstract

State feedback method is quite popular in control engineering field. However, some popular properties of state feedback approach cannot be used while any of the system states cannot be obtained beforehand. Therefore, this paper proposes a new observer design for a class of uncertain systems through sliding mode control theory. Based on strictly positive real concept, the stability of the equivalent error system is verified. Further, by using the generalized matrix inverse approach, the proposed switching term can drive the error states to zero, and it ensures the global reaching condition of the sliding mode of the error system. Moreover, the presented sliding mode observer is proposed to possess the invariance property to the uncertainty and/or external disturbance. Furthermore, the developed sliding mode observer is extended to release the limitation of knowing the bounds of the lumped perturbations in advance. That is, not only a new sliding mode observer but also a new adaptive sliding mode observer is proposed in this paper. Finally, three examples are illustrated to demonstrate the validity of the proposed sliding mode observer and the proposed adaptive sliding mode observer.

Variable structure observer design for a class of uncertain systems with a time-varying delay

“…Since their SMO design (Yan and Edwards, 2007;Spurgeon, 2008) is based on a state transformation, their results are indirectly obtained due to the requirement of coordinate transformation. Recently, using the generalized matrix inverse approach, Liu et al (2009) proposed a new SMO for a class of uncertain systems. However, none of the above SMO design considered the state delay factor.…”

“…In this paper, utilizing the results derived by Liu et al (2009) and VSC theory, the design of a new VSO for a class of uncertain systems with time-varying delay is accomplished. The proposed variable structure observer will be shown to possess the invariance property in relation to the lumped perturbation as the traditional variable structure controller does.…”

“…The purpose of this example is to demonstrate the effectiveness of the proposed VSO, and four different cases will be considered to show Unauthenticated Download Date | 5/11/18 1:08 AM Variable structure observer design for a class of uncertain systems with a time-varying delay 579 that the proposed VSO is superior to the traditional ones. The following dynamical system is adopted from Liu et al (2009), Walcott andŻak (1987 as well asŻak and Hui (1993), in which all the parameters are the same as their parameters except the time-varying delay term. The observers with and without considering the time-varying delay terms were simulated on a computer.…”

Decentralized Observer Design for a Class of Nonlinear Uncertain Large Scale Systems with Lumped Perturbations

“…Hassan [9] developed a state observer to estimate the states for nonlinear discrete-time dynamical systems with uncertain parameters. On the other hand, based on SMC theory, some design approaches and applications of sliding mode observer (SMO) [12][13][14][15][16][17][18][19][20][21][22] have been proposed. Trinh and Aldeen [11] proposed a simple and systematic design method to investigate a reducedorder state observer for large-scale discrete-time systems; their observer dynamics are derived based on a set of unstable and/or poorly damped eigenvalues of the system.…”

“…Recently, Liu et al [20] developed an observerbased fault-tolerant control scheme for Markovian jump systems with time delay and Lipschitz nonlinearities based on a new proportional and derivative SMO technique. And Liu et al [22] proposed a new SMO design for a class of uncertain systems via the generalized matrix inverse approach. And Liu et al [22] proposed a new SMO design for a class of uncertain systems via the generalized matrix inverse approach.…”