Dynamic output feedback control for Markovian jump systems with time-varying delays

Yu, Juebang; Tan, Jiacheng; Jiang, Haibo; Liu, Honghai

doi:10.1049/iet-cta.2011.0089

Cited by 21 publications

(9 citation statements)

References 29 publications

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“…To this end, it is assumed that the lower and upper bounds of time-delay are d 1 = 0.1 and d 2 = 1.1, respectively. It has been found that there is no feasible solution based on the delay-dependent approach presented in [31]. However, by applying Theorem 3 with ϵ 1 = ϵ 2 = 1, one indeed obtains the feasible solutions, and a detailed comparison of the obtained minimum H ∞ performance indices γ min by the mode-dependent nonrational controller (6) with different delay-derivatives and transition rate (TR) divisions is shown in Table 2, where unknown µ indicates the corresponding delay-derivative-independent controller design results, as mentioned in Remark 7, and K = 2, K = 3 and K = 4 represent that the TRM is divided evenly into two, three, and four sections with the mid-points of their upper and lower bounds by the sojourn-time fractionizing technique, respectively.…”

Section: Simulation Studiesmentioning

confidence: 99%

“…Note that most of the existing dynamic output feedback controller (DOFC) synthesis involves exclusively the rational controller for time-delay systems [28][29][30][31]. An attempt to design a nonrational controller [32], which is with a time-delay frame in the controller structure, seems more sensible and less conservative, since more information on time-delays is incorporated in the controller.…”

Section: Introductionmentioning

confidence: 99%

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Mode-dependent nonrational output feedback control for continuous-time semi-Markovian jump systems with time-varying delay

Wei

Qiu

2015

Nonlinear Analysis: Hybrid Systems

109

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Section: Simulation Studiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mode-dependent nonrational output feedback control for continuous-time semi-Markovian jump systems with time-varying delay

Wei

Qiu

2015

Nonlinear Analysis: Hybrid Systems

109

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“…Owing to the hybrid nature of reset control systems and the flow set and jump set are dependent on the output matrix uncertainty, the reset controller design is not easy. However, note that the dynamic output feedback (DOF) is used for the flow dynamics of the reset controller (5), and there exist some DOF design methods for linear systems (see [29][30][31]). Then, with the proposed stability conditions in this work, the reset controller can be designed based on the DOF design (i.e.…”

Section: Remarkmentioning

confidence: 99%

Stability and stabilisation of reset control systems with uncertain output matrix

Zhao

Wang

2015

IET Control Theory & Applications

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The stability analysis of reset control systems is challenging when reset time instants are uncertain, because such uncertainties may damage or even destabilise the system. This study considers reset control systems with uncertain output matrix, and presents sufficient conditions for the quadratic stability and finite gain L 2 stability of the closed-loop reset systems. Then, the results are extended to piecewise quadratic stability, which is much less conservative. The design of the reset controller is also discussed. All the results are given as linear matrix inequalities by using a lemma about multi-convex function. Several examples are given to show the effectiveness of the obtained results. IntroductionReset controllers were first proposed in [1], where the so-called Clegg integrator was introduced, the controller state is reset to zero when its input and output satisfy some pre-defined conditions. In [2], the Clegg integrator was generalised to first-order reset element (FORE), where it was suggested that introducing reset control may overcome some fundamental limitations and improve transient performance of linear control systems. An explicit example was given in [3] to say that some specifications can be met by reset controller but not by any linear time invariant (LTI) controllers, more explicit examples can be found in [4]. The FORE with zero crossing reset conditions was used to improve transient performance such as in [5][6][7]. Delay-dependent and delay-independent stability results of reset systems were given in [8-10], respectively. Well-posedness of reset control systems with and without reset band were considered in [11,12]. In [13,14], dissipativity theory was used for stability analysis of reset control systems. More results about zero-crossing resets can be found in [15] and references therein. In [16], a new model of FORE under the hybrid systems framework of [17] was proposed that allows jumps on more complicated sets, and temporal regularisation is introduced to avoid Zeno solutions. With this new model, the exponential stability and input-output stability were presented, and these results provide a systematic design tool for reset controllers. The L 2 stability result for reset control systems was first presented in [18]. Then, linear matrix inequality(LMI) conditions were given in [16] to estimate the L 2 gain and piecewise quadratic Lyapunov functions were used to get a tighter L 2 gain estimation. In [19] the analytical and numerical Lyapunov functions were provided to prove stability and L 2 gain performance of FORE control systems. Furthermore, the LMI-based analysis method was used to determine the performance of single-input-single-output (SISO) reset systems in both L 2 gain and H 2 sense as discussed in [20]. Recently, improved reset rules were proposed in [21] such that strictly decreasing Lyapunov functions at jumps can be constructed.Most of the above mentioned literature considered the control structure in Fig. 1 with certain system matrices. The control input signal is u and ...

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“…In order to obtain the main results in this paper, the following lemmas are needed: Lemma 3.1: [7] For any scalars M > 0, N > 0 , h(t) is a continuous function and satisfies h m < h(t) < h M , then…”

Section: Output Feedback Designmentioning

confidence: 99%

H<inf>∞</inf> fuzzy Networked control for vehicle lateral dynamics

Latrach

Kchaou

Rabhi

2013

21st Mediterranean Conference on Control and Automation

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A vehicle dynamics control system (NCS) has been developed in this study for improving vehicle yaw rate dynamics under unreliable communication links with packet dropouts, and network-induced delay which are two typical network constraints of unreliable transmission. The NCS system consists of a fuzzy H∞ static output feedback controller. After giving the nonlinear model of the vehicle, a TakagiSugeno (T-S) fuzzy model representation is first discussed. Next, based on the Lyapunov krasovskii functional approach and a parallel distributed compensation scheme, the gains of the fuzzy controller are determined in terms of Linear Matrix Inequality (LMI). Simulations have been conducted to evaluate performance of the closed loop system under limitation of the network resources caused by data transmission.

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Dynamic output feedback control for Markovian jump systems with time-varying delays

Cited by 21 publications

References 29 publications

Mode-dependent nonrational output feedback control for continuous-time semi-Markovian jump systems with time-varying delay

Mode-dependent nonrational output feedback control for continuous-time semi-Markovian jump systems with time-varying delay

Stability and stabilisation of reset control systems with uncertain output matrix

H<inf>∞</inf> fuzzy Networked control for vehicle lateral dynamics

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Dynamic output feedback control for Markovian jump systems with time-varying delays

Cited by 21 publications

References 29 publications

Mode-dependent nonrational output feedback control for continuous-time semi-Markovian jump systems with time-varying delay

Mode-dependent nonrational output feedback control for continuous-time semi-Markovian jump systems with time-varying delay

Stability and stabilisation of reset control systems with uncertain output matrix

H<inf>&#x221E;</inf> fuzzy Networked control for vehicle lateral dynamics

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H<inf>∞</inf> fuzzy Networked control for vehicle lateral dynamics