Stability of nonlinear time-varying digital 2-D Fornasini-Marchesini system

Kurek, Jan

doi:10.1007/s11045-012-0193-4

Cited by 42 publications

(19 citation statements)

References 11 publications

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“…In this study, the global asymptotic equilibrium point of the 2-D nonlinear system (1) is assumed to be 0. Please refer to Definitions 2, 3, and 4 in (Wang et al 2013) and Definitions 1, 2, 3, and 4 in (Kurek 2014)) for the definition of the global asymptotic equilibrium point.…”

Section: Problem Formulationmentioning

confidence: 99%

Sensor fault reconstruction for a class of 2-D nonlinear systems with application to fault compensation

Zhao

Zhou

Wang

2015

Multidim Syst Sign Process

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This paper considers the problem of sensor fault reconstruction and compensation for a class of two dimensional (2-D) nonlinear systems. The 2-D nonlinear system is described by the Fornasini-Marchesini local state-space second model with Lipschitz nonlinearity. The sensor fault considered in this study could be of arbitrary form and its size can be even unbounded. An integrated fault/state observer is proposed to obtain the asymptotic estimation of sensor faults and system states at the same time. A sufficient condition for the existence of the integrated observer is given in terms of linear matrix inequalities. H ∞ sensor fault estimation/reconstruction is also considered for the 2-D nonlinear system when there are both sensor faults and input disturbances. Based on the estimation of sensor faults, a sensor compensation scheme can be performed by subtracting the fault term from the measurement output, and the existing output feedback controller can run normally without the switchover of sensors or reconfiguration when sensor faults occur. An example is provided to illustrate the effectiveness of the proposed method for both sensor fault reconstruction and compensation.

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Section: Problem Formulationmentioning

confidence: 99%

Sensor fault reconstruction for a class of 2-D nonlinear systems with application to fault compensation

Zhao

Zhou

Wang

2015

Multidim Syst Sign Process

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“…The development of a stability theory for nonlinear 2D systems is underway, e.g., (Kurek, 2012;Yeganefar et al, 2013). Also sufficient conditions guaranteeing Lyapunov stability, asymptotic stability and exponential stability of nonlinear 2D differential-discrete systems were developed in (Knorn and Middleton, 2016), where the conditions for Lyapunov stability and asymptotic stability require that the corresponding 2D Lyapunov function has the negative semi-definite property.…”

Section: Introductionmentioning

confidence: 99%

Pass profile exponential and asymptotic stability of nonlinear repetitive processes

et al. 2017

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This paper considers discrete and differential nonlinear repetitive processes using the state-space model setting. These processes are a particular class of 2D systems that have their origins in the modeling of physical processes. Their distinguishing characteristic is that one of the two independent variables needed to describe the dynamics evolves over a finite interval and therefore they are defined over a subset of the upper-right quadrant of the 2D plane. The current stability theory for nonlinear dynamics assumes that they operate over the complete upper-right quadrant and this property may be too strong for physical applications, particulary in terms of control law design. With applications in mind, the contribution of this paper is the use of vector Lyapunov functions to characterize a new property termed pass profile exponential stability.

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“…For example, the stability of nonlinear deterministic systems described by a Fornasini-Marchesini model was analyzed in (Kurek, 2014). Discrete nonlinear systems described by the Roesser model were considered in Yeganefar et al (2013) where Lyapunov theorems to check for asymptotic and exponential stability were established and a converse Lyapunov theorem developed for exponential stability.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of 2D Roesser systems via vector Lyapunov functions

et al. 2017

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The paper gives new results that contribute to the development of a stability theory for 2D nonlinear discrete and differential systems described by a state-space model of the Roesser form using an extension of Lyapunov's method. One of the main difficulties in using such an approach is that the full derivative or its discrete counterpart along the trajectories cannot be obtained without explicitly finding the solution of the system under consideration. This has led to the use of a vector Lyapunov function and its divergence or its discrete counterpart along the system trajectories. Using this approach, new conditions for asymptotic stability are derived in terms of the properties of two vector Lyapunov functions. The properties of asymptotic stability in the horizontal and vertical dynamics, respectively, are introduced and analyzed. This new properties arise naturally for repetitive processes where one of the two independent variables is defined over a finite interval. Sufficient conditions for exponential stability in terms of the properties of one vector Lyapunov function are also given as a natural follow on from the asymptotic stability analysis.

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Stability of nonlinear time-varying digital 2-D Fornasini-Marchesini system

Cited by 42 publications

References 11 publications

Sensor fault reconstruction for a class of 2-D nonlinear systems with application to fault compensation

Sensor fault reconstruction for a class of 2-D nonlinear systems with application to fault compensation

Pass profile exponential and asymptotic stability of nonlinear repetitive processes

Stability analysis of 2D Roesser systems via vector Lyapunov functions

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