Robust state-derivative feedback LMI-based designs for time-varying delay system

Amri, Issam; Soudani, Dhaou; Benrejeb, Mohamed

doi:10.1109/ccca.2011.6031530

Cited by 5 publications

(6 citation statements)

References 13 publications

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“…In this section, to demonstrate the validity of the proposed method in this paper, we consider a VTOL vehicle example taken from [28,29]. The system state is x D OEx 1 x 2 x 3 x 4 T , where x 1 is the horizontal velocity in knot, x 2 is the vertical velocity in knot, x 3 is the pitch rate in degree per second, and x 4 is the pitch angle in degree.…”

Section: Numerical Examplesmentioning

confidence: 99%

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Active fault tolerant control systems by the semi‐Markov model approach

Huang

Shi

Xue

2013

Adaptive Control & Signal

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This paper investigates the active fault tolerant control problem via the H 1 state feedback controller. Because of the limitations of Markov processes, we apply semi-Markov process in the system modeling. Two random processes are involved in the system: the failure process and the fault detection process. Therefore, two corresponding semi-Markov processes are integrated in the closed-loop system model. This framework can generally accommodate different types of system faults, including the randomly happening sensor faults and actuator faults. A controller is designed to guarantee the closed-loop system stability with a prescribed noise/disturbance attenuation level. The controller can be readily solved by using convex optimization techniques. A vertical take-off and landing vehicle example with actuation faults is used to demonstrate the effectiveness of the proposed technique.represent the random variations of the system parameters. Normally, continuous-time finite state Markov processes are used in continuous-time systems where the system may jump at any time instants, whereas in discrete-time systems, discrete-time finite state Markov processes are applied, to be precise, only Markov process kernels are used. Sometimes, finite state processes are also called discrete-state processes, or countable state processes. To practically formulate active fault tolerant control problems, two stochastic processes are involved in the system model: one is used to model the system faults and the other one is used to represent the fault detection and identification (FDI) process [7]. The rationale behind the two-process model is that the FDI process brings random variations into the control law. In other words, the FDI process modifies the system dynamics by realizing the control strategy reconfiguration [8]. The two-process model was proposed in [9], where necessary and sufficient conditions were provided for systems with single component failures. For the system with multiple failure occurrences, the stochastic stability analysis was presented in [10]. Further, considering the system uncertainties, detection delays, and noise/disturbances, results have been reported in [11]. Besides the results on the stability issue, optimal controller design problems have been studied for fault tolerant control systems modeled by Markov processes (see [12] and the references therein).Among the aforementioned works, most of them deploy continuous-time or discrete-time Markov processes to model the system failure. To satisfy the requirements of Markov processes, the life time of the system components should be assumed to be exponentially distributed. However, such an assumption may not be appropriate in practice for two reasons. Firstly, in the reliability engineering, a typical transition/failure rate function is in a bath tube shape instead of a constant value [13,14]. With such shapes of transition/failure rates, the system components would be more likely to fail in the 'infant' or 'senior' stage. For a more comprehensive literature rev...

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Section: Numerical Examplesmentioning

confidence: 99%

“…For each round of simulation, the semi-Markov processes Á t and r t are randomly generated according to the transition rate matrices in (28). For each round of simulation, the semi-Markov processes Á t and r t are randomly generated according to the transition rate matrices in (28).…”

Section: Numerical Examplesmentioning

confidence: 99%

Active fault tolerant control systems by the semi‐Markov model approach

Huang

Shi

Xue

2013

Adaptive Control & Signal

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“…The solutions of LMI (20) . Figure 1 displays the states of the differential equations of system (42) by using the nonlinear state feedback controller (4).…”

Section: Example A: Unstable Nonlinear Numerical Systemmentioning

confidence: 99%

“…In [19], a nonlinear matrix inequality is employed as a stabilization condition for uncertain time-delayed linear systems. In [20], the robust exponential stabilization problem based on the Lyapunov parameter-dependent function and LMIs for a class of uncertain systems with time-varying delays is investigated. In [21], the stabilization problem of a two-dimensional Burgers equation around a stationary solution using nonlinear feedback boundary controller is investigated.…”

Section: Introductionmentioning

confidence: 99%

A Robust LMI Approach on Nonlinear Feedback Stabilization of Continuous State-Delay Systems with Lipschitzian Nonlinearities: Experimental Validation

Mobayen

Pujol

2018

Iran J Sci Technol Trans Mech Eng

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This paper suggests a novel nonlinear state feedback stabilization control law using linear matrix inequalities for a class of time-delayed nonlinear dynamic systems with Lipschitz nonlinearity conditions. Based on the Lyapunov-Krasovskii stability theory, the asymptotic stabilization criterion is derived in the linear matrix inequality form and the coefficients of the nonlinear state-feedback controller are determined. Meanwhile, an appropriate criterion to find the proper feedback gain matrix F is also provided. The robustness purpose against nonlinear functions and time-delays is guaranteed in this scheme. Moreover, the problem of robust H ∞ performance analysis for a class of nonlinear time-delayed systems with external disturbance is studied in this paper. Simulations are presented to demonstrate the proficiency of the offered technique. For this purpose, an unstable nonlinear numerical system and a rotary inverted pendulum system have been studied in the simulation section. Moreover, an experimental study of the practical rotary inverted pendulum is provided. These results confirm the expected satisfactory performance of the suggested method.

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“…Less conservative LMI conditions were developed in Silva, Assunção, Teixeira, Faria, and Buzachero (2011), Silva, Assunção, Teixeira, and Buzachero (2012) by using parameter-dependent Lyapunov functions. LMI formulations for time delay systems have also been reported (Amri, Soudani, & Benrejeb, 2011;Jing, Shen, Dimirovski, & Jiang, 2009).…”

Section: Introductionmentioning

confidence: 97%

Direct discrete time design of robust state derivative feedback control laws

Rossi

Galvão

Teixeira

et al. 2016

International Journal of Control

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This paper is concerned with the problem of designing robust state derivative feedback control laws in discrete time. The main contribution consists of a method for recasting a continuous time state space model in the form of a discrete time model formulated in terms of the state derivative. Uncertain input delays and parametric uncertainties in polytopic form can be propagated from the original state space representation to the resulting state derivative model. Therefore, robust control techniques originally developed for discrete time state space models can be directly employed to design the state derivative feedback law. Three computational examples are presented for illustration. The first example highlights the importance of accounting for the effect of sampling in the design procedure. More specifically, a linear quadratic regulation problem involving the state derivative is addressed. The second example involves the design of a robust predictive controller in the presence of input constraints and uncertain time delay. Finally, the third example is concerned with robust pole placement in the presence of parametric uncertainty.

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Robust state-derivative feedback LMI-based designs for time-varying delay system

Cited by 5 publications

References 13 publications

Active fault tolerant control systems by the semi‐Markov model approach

Active fault tolerant control systems by the semi‐Markov model approach

A Robust LMI Approach on Nonlinear Feedback Stabilization of Continuous State-Delay Systems with Lipschitzian Nonlinearities: Experimental Validation

Direct discrete time design of robust state derivative feedback control laws

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