Stabilization of Markovian jump systems with incomplete knowledge of transition probabilities and input quantization

Park, Bum Yong; Kwon, Nam Kyu; Park, PooGyeon

doi:10.1016/j.jfranklin.2015.06.008

Cited by 28 publications

(22 citation statements)

References 22 publications

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“…A performance comparison between dynamical uniform and static logarithmic SMC quantizers is carried out in the work of Liu et al In order to classify fast and slow phenomena incurred by Markov process and slow disturbances, respectively, Abdel‐Galil et al utilize a vector quantization to convert the continuous observation into sequences of discrete one. The input quantization between controller and plant is analyzed in the work of Park et al To offset the adverse influence of input saturation, dead zone, and signal quantization, a dynamical adaptive SMC compensator is put forward in the work of Zheng and Yang …”

Section: Introductionmentioning

confidence: 99%

Sliding mode control of time‐varying delay Markov jump with quantized output

Zhang

Shen

2018

Optim Control Appl Methods

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This paper investigates the quantized sliding mode control of Markov jump systems with time-varying delay. A dynamical adjustment law is explored to quantize the system output. By constructing an observer-based integral sliding surface, a sliding mode controller is designed to take over the dynamical motion of state estimation and ensure the reachability of sliding surface. A new scaling manner is developed to build the bound between the system output and quantized error. With the help of separation strategies for controller synthesis and general transition probabilities and a lower bound theorem for nonlinear integral terms, a new synthesis method to ensure the required stability and meet the required  ∞ performance is proposed in the form of linear matrix inequalities. The validity of the proposed control method is illustrated by a numerical example. KEYWORDS ∞ control, Markov jump system, quantized control, sliding mode control INTRODUCTIONRecently, much attention has been devoted to the field of Markov jump systems (MJSs). This kind of system is extensively applied in many practical fields, such as flight control systems, network control systems, and manufacturing systems. Transition probabilities (TPs), which illustrate the possibility of switching among system modes, have direct impact on system behavior. By now, most of the existing results are assumed that they are known. However, this assumption is hard to be realized due to challenges like accuracy of measuring methods and environment conditions. 1 Hence, from the perspective of engineering applications, MJSs with general TPs are investigated in other works. [2][3][4][5][6] On the other hand, in physical processes, time delay is unavoidable and should be taken into account in the stage of controller design. 7 As a consequence, a dynamic output feedback control of MJSs with time delay is considered in the work of Boukas et al. 8 Xu et al 9 obtain a stochastic stability with the prescribed  ∞ performance via a bounded real lemma and slack matrix variables. An input-output model by substituting a feedback interconnection formulation for the time-delayed filtering error MJSs is proposed in the work of Wei et al. 10 Zhang et al 11 use a mode-dependent Lyapunov-Krasovskii functional that includes tripe integrals term to provide the stability conditions. This result is further extended in the work of Luan et al, 12 which studies the finite-time  ∞ control subject to the average dwell-time constraint for discrete case.Sliding mode control (SMC) is an effective measurement to deal with system uncertainties. This technique has been proved to have features such as fast response and insensitive to variations in internal and external disturbances. [13][14][15] Numerous achievements about SMC for stochastic system have been published, especially for MJSs; see other works [16][17][18][19][20][21][22] 226

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Section: Introductionmentioning

confidence: 99%

Sliding mode control of time‐varying delay Markov jump with quantized output

Zhang

Shen

2018

Optim Control Appl Methods

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“…Because of two kinds of mechanisms contained, it is very suitable to model such actual systems whose structures or parameters change [1,2]. Over the past years, many research topics on MJSs have been extensively studied, like stability analysis [3][4][5][6], stabilization [7][8][9][10][11], robust control [12][13][14][15], adaptive control [16][17][18][19], ∞ filtering and control [20,21], state estimation [22][23][24][25], synchronization [26][27][28][29][30], and so on.…”

Section: Introductionmentioning

confidence: 99%

Observer Design for Delayed Markovian Jump Systems with Output State Saturation

Wang

Feng

2018

Mathematical Problems in Engineering

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This paper considers the observer design problem of continuous-time delayed Markovian jump systems with output state saturation. Different from the traditionally observer-based saturation control methods, a kind of system output state saturation with a partially delay-dependent property is proposed, where both nondelay and delay states exist at the same time but happen asynchronously. By exploiting the Bernoulli variable, the probability distributions of such two states are described and considered in the observer design. Based on an improved equality applied to deal with saturation terms, sufficient conditions for the designed observer with three kinds of output saturations are all provided with LMI forms. Finally, a numerical example is given to indicate the effectiveness of the obtained results.

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“…Recently, several interesting results on stability, stabilisation and filtering problems for MJSs with partly unknown transition probabilities have been addressed. For example, we refer readers to [13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

An adaptive sliding mode approach for Markovian jump systems with uncertain mode-dependent time-varying delays and partly unknown transition probabilities

Zohrabi

Zakeri

Abolmasoumi

et al. 2018

Int. J. Dynam. Control

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This paper deals with the problems of stochastic stability and sliding mode control for a class of continuous-time Markovian jump systems with mode-dependent time-varying delays and partly unknown transition probabilities. The design method is general enough to cover a wide spectrum of systems from those with completely known transition probability rates to those with completely unknown transition probability rates. Based on some mode-dependent Lyapunov-Krasovski functionals and making use of the freeconnection weighting matrices, new delay-dependent conditions guaranteeing the existence of linear switching surfaces and the stochastic stability of sliding mode dynamics are derived in terms of linear matrix inequalities (LMIs). Then, a sliding mode controller is designed such that the resulted closed-loop system's trajectories converge to predefined sliding surfaces in a finite time and remain there for all subsequent times. This paper also proposes an adaptive sliding mode controller design method which applies to cases in which modedependent time-varying delays are unknown. All the conditions obtained in this paper are in terms of LMI feasibility problems. Numerical examples are given to illustrate the effectiveness of the proposed methods.

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Stabilization of Markovian jump systems with incomplete knowledge of transition probabilities and input quantization

Cited by 28 publications

References 22 publications

Sliding mode control of time‐varying delay Markov jump with quantized output

Sliding mode control of time‐varying delay Markov jump with quantized output

Observer Design for Delayed Markovian Jump Systems with Output State Saturation

An adaptive sliding mode approach for Markovian jump systems with uncertain mode-dependent time-varying delays and partly unknown transition probabilities

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