Design of the Observer Feedback Gain for Two-Dimensional Discrete Systems

Asian Journal of Control

2016

Many valuable properties of the state feedback method can not be applied to some class of control systems while some of the system states cannot be measured directly. An attractive alternative approach is to make good use of a state observer. In this paper, a new decentralized sliding mode observer (DSMO) is proposed for a class of nonlinear uncertain large-scale systems (LSS) with lumped perturbations based on the sliding mode control (SMC) theory. Our main result presented here is that we introduce a new switching term to the traditional LSS observer design for a class of large-scale system to generate a new decentralized sliding mode observer. The generalized matrix inverse concept is adopted to avoid using the un-measurable state and the global reaching condition of the sliding mode for each error subsystem is guaranteed. The stability of each equivalent error subsystem is verified based on the strictly positive real concept. It also shows that the investigated uncertain large-scale systems still possesses the property of insensitivity to the lumped perturbations as does the traditional linear system. Moreover, the state transformation approach is no longer needed as there is no longer concern about the problems of finding a suitable transformation or indirect estimated states, since the proposed DSMO is not based on the transformed system model. Finally, a numerical example with a series of computer simulations is given to demonstrate the validity of the proposed decentralized sliding mode observer. . His research interests include variable structure systems, sliding mode control, large-scale systems, time delayed systems, non-linear systems and uncertain systems.

Section: Proof Consider the Following Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Asian Journal of Control

2016

“…For example, Karafyllis and Kravaris (2007) studied the construction of observers for time-varying discrete-time systems and proposed some appropriate notions of robust complete observability. Liu (2004) proposed an algorithm for state observer design of two-dimensional linear shift-invariant systems via using the well-known one-dimensional system results. Röbenack and Lynch (2006) proposed two methods for nonlinear observer design which are based on a partial nonlinear observer canonical form.…”

Section: X(t) = (A + δA)x(t) + (A D + δA D )X(t − τ ) + (B + δB)u(t) mentioning

confidence: 99%

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

International Journal of Applied Mathematics and Computer Science

2012

Design of a state observer is an important issue in control systems and signal processing. It is well known that it is difficult to obtain the desired properties of state feedback control if some or all of the system states cannot be directly measured. Moreover, the existence of a lumped perturbation and/or a time delay usually reduces the system performance or even produces an instability in the closed-loop system. Therefore, in this paper, a new Variable Structure Observer (VSO) is proposed for a class of uncertain systems subjected to a time varying delay and a lumped perturbation. Based on the strictly positive real concept, the stability of the equivalent error system is verified. Based on the generalized matrix inverse approach, the global reaching condition of the sliding mode of the error system is guaranteed. Also, 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. Furthermore, two illustrative examples with a series of computer simulation studies are given to demonstrate the effectiveness of the proposed design method.

“…Also, the significant advance in the observer theory may refer to Reference [8]. In addition, many observer design techniques have been proposed in References [9][10][11][12]. Based on the new parameterization of the generalized Sylvester equations solutions, Darouach and Boutat-Baddas [9] considered the observer 1342 W.-J.…”

Section: Introductionmentioning

confidence: 99%

Adaptive sliding mode observer design for a class of uncertain systems

Adaptive Control & Signal

2014

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.