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Robust stabilisation for non-linear time-delay semi-Markovian jump systems via sliding mode control
Qi, Wenhai,Park, Ju H.,Cheng, Jun,Kao, Yonggui IET 2017 IET CONTROL THEORY AND APPLICATIONS Vol.11 No.10
<P>This study deals with the problem of robust stabilisation for non-linear time-delay semi-Markovian jump systems via sliding mode control (SMC). Such a switching is governed by a semi-Markovian process which is time-varying and dependent on the sojourn-time <I>h</I>. The time delay is considered as time-varying and meets the requirements of the upper and lower bounds. By introducing free-connection weighting matrix method and Lyapunov functional, sufficient conditions for the resulting sliding mode dynamics in the form of linear matrix inequalities are derived to guarantee the closed-loop system robustly stochastically stable for all admissible uncertainties and non-linear perturbations. Then, an SMC law is synthesised to drive the system trajectories onto the predefined switching surface in a finite time. Finally, an example illustrates the validity of the obtained results.</P>
Wenhai Qi,Xianwen Gao 제어·로봇·시스템학회 2016 International Journal of Control, Automation, and Vol.14 No.6
The paper is concerned with the problem of positive L1-gain filter design for positive continuous-timeMarkovian jump systems with partly known transition rates. Our aim is to design a positive full-order filter such thatthe corresponding filtering error system is positive and stochastically stable with L1-gain performance. By applyinga linear co-positive Lyapunov function and free-connection weighting vectors, the desired positive L1-gain filter isprovided. The obtained theoretical results are demonstrated by numerical examples.
L1 Control for Positive Markovian Jump Systems with Partly Known Transition Rates
Wenhai Qi,Xianwen Gao 제어·로봇·시스템학회 2017 International Journal of Control, Automation, and Vol.15 No.1
This paper deals with the problem of L1 control for positive Markovian jump systems with partly knowntransition rates. First, by constructing an appropriate linear co-positive type Lyapunov-Krasovskii function, stochasticstability for the underlying system is discussed. Then, the L1-gain performance is analyzed. Based on the resultsobtained, an effective method is proposed for the design of state feedback controller. All the proposed conditionsare derived to ensure that the closed-loop Markovian jump system positive and stochastically stable with L1-gainperformance in linear programming. Finally, an example is given to demonstrate the validity of the main results.
Wenhai Qi,Yonggui Kao,Xianwen Gao 제어·로봇·시스템학회 2017 International Journal of Control, Automation, and Vol.15 No.5
The paper deals with the problems of passivity and passification for stochastic systems with Markovianswitching and generally uncertain transition rates. The considered systems are more general, which cover uncertaintransition rates and partly known transition rates as two special cases. By employing the multiple Lyapunov functionand some free-weighting matrices, a state feedback controller is constructed such that the resulted closed-loopsystem is stochastically passive. Some sufficient conditions for the solution to the problem are derived in the formof linear matrix inequalities (LMIs). Finally, a numerical example is given to demonstrate the validity of the mainresults.
<sub> L 1 </sub> finite-time stabilization for positive semi-Markovian switching systems
Qi, Wenhai,Park, Ju H.,Zong, Guangdeng,Cheng, Jun Elsevier science 2019 Information sciences Vol.477 No.-
<P><B>Abstract</B></P> <P>This paper investigates robust finite-time stabilization scheme for positive semi-Markovian switching systems (S-MSSs). Semi-Markovian process (SMP), external disturbances, and transient performances at a finite-time level may appear in a controlled system. A more general system model for S-MSSs that covers Markovian switching systems (MSSs) as a special case is suitable for describing some complex systems that are subject to random abrupt changes in structure and parameter. The main motivation for this is that finite-time problems can be used to describe the transient performance of practical industrial control processes. First, under the framework of stochastic semi-Markovian Lyapunov functions theory, some sufficient conditions for finite-time boundedness (FTBs) and <SUB> L 1 </SUB> FTBs criteria for positive S-MSSs are proposed for all admissible disturbances. Then, a novel <SUB> L 1 </SUB> finite-time controller design method that employs the gain matrix decomposition method is presented to reduce some conservativeness, thereby guaranteeing that the resulting closed-loop system (RLCS) could achieve positivity, FTBs, and attain a prescribed <SUB> L 1 </SUB> noise attenuation performance index in standard linear programming (LP). Finally, a practical example is introduced to show the effectiveness of the main theory</P>
Yujing Jin,Wenhai Qi,Guangdeng Zong 제어·로봇·시스템학회 2021 International Journal of Control, Automation, and Vol.19 No.6
In this paper, the finite-time synchronization (FTS) of semi-Markov neural networks (S-MNNs) with time-varying delay is presented. According to the Lyapunov stability theory, a mode-dependent LyapunovKrasovskii functional (LKF) is constructed. Compared with the traditional static event triggered scheme (ETS), a dynamic ETS is adopted to adjust the amount of data transmission and reduce the network burden. By using thegeneral free-weighting matrix method (F-WMM) to estimate a single integral term, a less conservative conclusion is proposed in standard linear matrix inequalities (LMIs). Finally, under the comparison of the static ETS and the dynamic ETS, a simulation example verifies the superiority of this method.
Asynchronous H∞ Control for Positive Discrete-time Markovian Jump Systems
Hui Shang,Wenhai Qi,Guang-Deng Zong 제어·로봇·시스템학회 2020 International Journal of Control, Automation, and Vol.18 No.2
This paper deals with the asynchronous H∞ control for discrete-time positive Markovian jump systems (PMJSs). In previous results about PMJSs, asynchronous behaviors are always overlooked and the designed controller is based on the synchronization between the system modes and controller modes. Sufficient conditions for stochastic stability are proposed by the use of Lyapunov-Krasovskii functional. The asynchronous controller is designed to ensure the closed-loop system stochastically stable with a prescribed H∞ performance index. All the conditions are given in linear matrix inequality framework. Finally, a pest’s age-structured population dynamic model is illustrated to show the validity of the present design.
Stochastic Stability, ℒ1-gain and Control Synthesis for Positive Semi-Markov Jump Systems
Longjiang Zhao,Wenhai Qi,Lihua Zhang,Yonggui Kao,Xianwen Gao 제어·로봇·시스템학회 2018 International Journal of Control, Automation, and Vol.16 No.5
This paper treats the problems of stochastic stability, ℒ1-gain and control synthesis for positive semi- Markov jump systems (S-MJSs). The system under consideration involves semi-Markov stochastic process related to Weibull distribution. The main motivation for this paper is that the positive condition sometimes needs to be considered in S-MJSs and the controller design methods in the existing works have some conservation. To deal with these problems, some sufficient conditions for stochastic stability of positive S-MJSs are established by implying the linear co-positive Lyapunov function. Then, some sufficient conditions for ℒ1-gain constraint are also presented, upon which, a state feedback controller is designed by decomposing the controller gain matrix such that the resulting closed-loop system is positive and stochastically stable with ℒ1-gain performance in the form of standard linear programming (LP). The advantages of the new framework lie in the following facts: (1) the weak infinitesimal operator is derived for S-MJSs under the constraint of positive condition and (2) the less conservative stabilizing controller is designed to achieve the desired control performance. Finally, numerical examples are given to demonstrate the validity of the main results.
Jiyang Wang,Wenhai Qi,Xianwen Gao,Yonggui Kao 제어·로봇·시스템학회 2017 International Journal of Control, Automation, and Vol.15 No.2
The paper is concerned with positive observer design for positive Markovian jump systems with incompletetransition rates and time delays that are mode-dependent and time-varying. Firstly, by applying an appropriateco-positive type Lyapunov-Krasovskii function and free-connection weighting vectors, sufficient conditions areproposed to ensure stochastic stability of the error positive system and existence of the positive observer. All theproposed conditions are derived in linear programming. Finally, an example is given to demonstrate the validity ofthe main results.
New Results on Finite-time Stabilization for Stochastic Systems with Time-varying Delay
Lihua Zhang,Wenhai Qi,Yonggui Kao,Xianwen Gao,Longjiang Zhao 제어·로봇·시스템학회 2018 International Journal of Control, Automation, and Vol.16 No.2
The paper deals with the problem of finite-time stabilization for stochastic systems with time-varying delay by defining a new criterion for finite-time stability. Firstly, by use of more appropriate Lyapunov-Krasovskii functional (LKF), the difficulties of finite-time stability confronted in system analysis and synthesis can be overcome. Then, a state feedback controller is constructed to guarantee the closed-loop system finite-time stable. New conditions for finite-time stability analysis as well as controller synthesis are established in terms of linear matrix inequality (LMI). Finally, two practical examples demonstrate the validity of the main results.