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

Abstract

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

Sliding mode control of Lorenz chaotic system of fluid thermal convection between infinite plates based on LMI

“…For fractional order nonlinear systems with uncertainties and external disturbances, a switched sliding mode control technology is proposed for control and chaos suppression in Majid et al, 32 In addition, there are some studies on sliding mode control based on LMI. For example, based on the sliding mode control of the vehicle speed system, the tracking problem and stability of vehicle speed system are studied in Gao et al 33 For the problem of vertical tail damage, an adaptive sliding mode fault-tolerant control method is proposed in Zhuang et al 34 Zhang and Shen 35 investigate the quantized sliding mode control of Markov jump systems with time-varying delay, a dynamical adjustment law is explored to quantize the system output. These methods used in the above literature are relatively novel.…”

Stabilization of two kinds of nonhomogeneous Markovian jump systems via sliding mode control

“…A SMC law was proposed for the networked MJSs subject to partly unknown transition probabilities 21 . The SMC technique was investigated for time‐varying delay Markov jump system with quantized output 22 . Based on a new sliding function, a SMC law was derived for continuous‐time MJSs with delays by using the asynchronous approach 23 .…”

“…21 The SMC technique was investigated for time-varying delay Markov jump system with quantized output. 22 Based on a new sliding function, a SMC law was derived for continuous-time MJSs with delays by using the asynchronous approach. 23 The asynchronous SMC issue was studied for two-dimensional MJSs.…”

Asynchronous control of T‐S fuzzy chaotic systems via a unified model using the hidden Markov model subject to strict dissipativity

“…Markovian jumping parameters often come from random factors such as sudden changes during the operation of the system, mutations in the connection of internal subsystems and the damage to system components. Therefore, Markovian jumping systems are studied, which provide the theoretical basis for solving engineering problems . The control for T‐S fuzzy Markovian jump systems was analyzed and researched .…”

“…Therefore, Markovian jumping systems are studied, which provide the theoretical basis for solving engineering problems. [2][3][4][5] The control for T-S fuzzy Markovian jump systems was analyzed and researched. 6,7 Besides, to improve the modeling ability of traditional Markovian jump systems, some questions about semi-Markovian jump systems were discussed.…”