Article
Automation & Control Systems
Xi-Kui Liu, Ji-Jing Zhuang, Yan Li
Summary: This paper investigates the H-infinity filtering problem of stochastic linear systems with Markovian jump and multiplicative noise, constructing a unified form of filters and deriving sufficient conditions for stochastic stability and H-infinity performance. The filter design with less coupling matrices and filter gain matrices calculation through linear matrix inequalities are presented, followed by three examples demonstrating the effectiveness of the proposed method.
INTERNATIONAL JOURNAL OF CONTROL AUTOMATION AND SYSTEMS
(2021)
Article
Automation & Control Systems
Meng Sun, Guangming Zhuang, Jianwei Xia, Qian Ma, Guoliang Chen
Summary: This article investigates robust dynamic output feedback stabilization for uncertain time-varying delays singular Markovian jump systems. It provides sufficient conditions of robust admissibility for unforced nominal time-varying delays SMJSs by using improved Lyapunov-Krasovskii functional. The robust DOF stabilization problem is solved by constructing a DOF controller that satisfies robust admissibility. The practicality of the results is demonstrated through numerical and practical examples.
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
(2022)
Article
Automation & Control Systems
Meng Zhao, Zhiru Cao, Yekai Yang, Yugang Niu
Summary: This work develops a finite-time sliding mode control (SMC) design for Markovian jump systems with peak-bounded external disturbances, taking into account the channel fading and deception attacks. A multiplicative fading model is introduced to describe the fading phenomenon in the unpredictable communication network, and the channel coefficients are independent random variables within certain intervals. By devising a sliding surface involving fading parameter and designing a security finite-time SMC law, the finite-time reachability of the specified sliding surface is achieved. Moreover, a partitioning strategy is adopted during the reaching phase and sliding phase of SMC design to achieve stochastic finite-time boundedness. Numerical simulation results demonstrate the effectiveness of the developed finite-time SMC approach under fading communication and malicious attacks.
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
(2023)
Article
Mathematics, Applied
Baoping Jiang, Zhengtian Wu, Hamid Reza Karimi
Summary: This paper investigates the mean-square stability analysis problem of Markovian jump systems with generally unknown and uncertain transition rates. Two methods are provided to handle the case where the transition rates from one mode to others are totally unknown using transition rate estimation. Five cases in the transition rates matrix are studied, covering almost all types of generally unknown and uncertain transition rates. Corresponding conditions for checking the mean-square stability of the considered systems are developed for these cases.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Computer Science, Theory & Methods
Yingying Han, Shaosheng Zhou
Summary: This paper investigates the extended dissipative filtering problem for a class of Markovian jump interval-valued fuzzy systems with uncertain transition rates. It provides a sufficient condition for stochastic asymptotic stability and extended dissipativity, and designs an extended dissipative filter via the Projection Lemma. The effectiveness of the proposed approach is demonstrated through two numerical examples.
FUZZY SETS AND SYSTEMS
(2021)
Article
Automation & Control Systems
Wenbin Chen, Fang Gao, Shengyuan Xu, Yongmin Li, Yuming Chu
Summary: This paper establishes a new Lyapunov-Krasovskii functional with state decomposition components to obtain sufficient mean-square exponentially admissible conditions for uncertain singular Markovian jump systems with time-varying delays. Based on these criteria, the robust mean-square exponentially admissible conditions for the systems are explored and a dynamic-output-feedback controller is designed. A robust mean-square stabilization criterion utilizing linear matrix inequality is derived through a state decomposition recombination approach. The superiority and feasibility of the proposed method are demonstrated through numerical examples.
SYSTEMS & CONTROL LETTERS
(2023)
Article
Automation & Control Systems
Guifang Cheng, Yuanyuan Ju, Xiaowu Mu
Summary: This paper explores the stochastic finite-time stability and state feedback controller design for linear semi-Markovian jump systems with generally uncertain transition rates. A sufficient condition is established using a stochastic Lyapunov functional, and a state feedback controller is obtained based on linear matrix inequality conditions to ensure finite-time stabilization. Numerical examples are provided to demonstrate the effectiveness of the proposed method.
INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE
(2021)
Article
Automation & Control Systems
Chi Zhang, Jun-Guo Lu
Summary: This article investigates the robust stochastic stability problem and robust H-2 performance problem of discrete-time Markovian jump linear systems with uncertain transition probabilities. Perturbation bounds for robust stochastic stability are obtained using the Kronecker product and mu analysis. The problem is transformed into the judgment of the nonsingularity of uncertain matrices. Exact upper and lower bounds for robust H-2 performance are also obtained. A sufficient and necessary condition for guaranteeing robust H-2 performance is derived. The results are given in terms of the structured singular value, and numerical examples are provided to demonstrate the effectiveness of the proposed results.
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
(2023)
Article
Computer Science, Information Systems
Jiahui Wang, Yabin Gao, Yifan Liu, Jianxing Liu, Guanghui Sun, Ligang Wu
Summary: This paper explores the dynamic practical-sliding-mode control and estimation of unknown functions for singular Markovian jump systems with system perturbations. It proposes an intelligent dynamic practical sliding mode control method based on ellipsoidal-type interval type-2 fuzzy neural networks, and proves its stability and performance.
INFORMATION SCIENCES
(2022)
Article
Mathematics, Applied
Ngoc Hoai An Nguyen, Sung Hyun Kim
Summary: This paper proposes a method for asynchronous mode-dependent dissipative control, using control-mode-dependent Lyapunov functions to address the control problem of continuous-time semi-Markovian jump systems. By reducing the block size of stabilization conditions, the control system performance is further improved, and non-convex terms are explicitly addressed.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Automation & Control Systems
Wei Kang, Jun Cheng, Xia Zhou, Jinde Cao, Hailing Wang
Summary: This work investigates the asynchronous quantized control of discrete-time Markovian switching Lur'e systems with an event-triggered mechanism. It employs a hidden Markov model to model the asynchronous controller and quantization effects, deriving sufficient conditions by choosing a proper stochastic Lyapunov functional. A practical example is provided to demonstrate the effectiveness and efficiency of the proposed method.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2021)
Article
Computer Science, Information Systems
Won Il Lee, Bum Yong Park
Summary: This study presents a controller design approach for stabilizing Markovian jump systems, utilizing a two-part controller that combines linear and nonlinear control components, and employing partial transition rate information to reduce conservatism. The effectiveness of the proposed controller is demonstrated through numerical examples.
Article
Automation & Control Systems
Yufeng Tian, Zhanshan Wang
Summary: This paper investigates the stochastic stability of Markovian jump systems with unified uncertain transition rates using multiple integral techniques. A novel Lyapunov-Krasovskii functional is constructed, containing more integral terms than existing ones. An auxiliary function-based multiple integral inequality is proposed to obtain a tighter bound of the Lyapunov-Krasovskii functional, and a new stability condition is derived. The effectiveness of the approach is demonstrated through examples.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2022)
Article
Computer Science, Information Systems
Huasheng Zhang, Jianwei Xia, Guangming Zhuang, Hao Shen
Summary: This paper addresses the problem of robust H-infinity state feedback control with interval pole constraints for uncertain stochastic Markovian jump systems (MJSs). The paper presents sufficient conditions for robust interval stability using a linear operator and its spectrum, and designs robust interval stabilization controller and robust H-infinity controller to ensure system stability and adjust the rate of convergence.
SCIENCE CHINA-INFORMATION SCIENCES
(2022)
Article
Computer Science, Information Systems
Qingdong Sun, Junchao Ren, Jun Fu
Summary: This work studies the problem of sliding mode preview control (SMPC) for a class of uncertain discrete-time T-S fuzzy Markovian jump system (MJS) subject to time-varying delays. Due to the existence of the Markovian chain and uncertain time-varying coefficients, a traditional difference method is no longer applicable. To overcome this issue, an approach combining the robust control technique is adopted. The sliding mode preview controller is synthesized based on a mode-independent sliding surface to guarantee the stochastic stability of the quasi-sliding motion (QSM) and the reachability of a sliding region.
INFORMATION SCIENCES
(2023)