scholarly journals ℋ∞Control for Two-Dimensional Markovian Jump Systems with State-Delays and Defective Mode Information

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Yanling Wei ◽  
Mao Wang ◽  
Hamid Reza Karimi ◽  
Jianbin Qiu
Keyword(s):  
State Feedback ◽  
Transition Probabilities ◽  
Linear Time ◽  
Design Method ◽  
Transition Probability ◽  
State Feedback Control ◽  
Delay Systems ◽  
Linear Matrix ◽  
Two Dimensional ◽  
Markovian Jump

This paper investigates the problem ofℋ∞state-feedback control for a class of two-dimensional (2D) discrete-time Markovian jump linear time-delay systems with defective mode information. The mathematical model of the 2D system is established based on the well-known Fornasini-Marchesini local state-space model, and the defective mode information simultaneously consists of the exactly known, partially unknown, and uncertain transition probabilities. By carefully analyzing the features of the transition probability matrices, together with the convexification of uncertain domains, a newℋ∞performance analysis criterion for the underlying system is firstly derived, and then theℋ∞state-feedback controller synthesis is developed via a linearisation technique. It is shown that the controller gains can be constructed by solving a set of linear matrix inequalities. Finally, an illustrative example is provided to verify the effectiveness of the proposed design method.

Optimal H2 and H∞ Mode-Independent Control for Generalized Bernoulli Jump Systems

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
A. R. Fioravanti ◽  
A. P. C. Gonçalves ◽  
J. C. Geromel
Keyword(s):  
State Feedback ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Random Variable ◽  
Transition Probability Matrix ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Availability Constraints ◽  
Partial Mode ◽  
Jump Systems

This paper deals with state-feedback control of discrete-time linear jump systems. The random variable representing the system modes has a generalized Bernoulli distribution, which is equivalent to a Markov chain where the transition probability matrix has identical rows. Another assumption is about the availability of the mode to the controller. We derive necessary and sufficient linear matrix inequalities (LMI) conditions to design optimal H2 and H∞ state-feedback controllers for the particular class of transition probabilities under consideration and subject to partial mode availability constraints or equivalently cluster availability constraints, which include mode-dependent and mode-independent designs as particular cases. All design conditions are expressed in terms of LMIs. The results are illustrated through a numerical example.

Further enhancement on H∞ sliding mode control design for singular Markovian jump systems with partly known transition probabilities

2021 ◽  
pp. 107754632198920
Author(s):  
Zeinab Fallah ◽  
Mahdi Baradarannia ◽  
Hamed Kharrati ◽  
Farzad Hashemzadeh
Keyword(s):  
Transition Probabilities ◽  
Sliding Mode ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Linear Matrix ◽  
Sliding Mode Controller ◽  
Sliding Surface ◽  
Markovian Jump ◽  
Markovian Jump System ◽  
Singular Markovian Jump Systems

This study considers the designing of the H ∞ sliding mode controller for a singular Markovian jump system described by discrete-time state-space realization. The system under investigation is subject to both matched and mismatched external disturbances, and the transition probability matrix of the underlying Markov chain is considered to be partly available. A new sufficient condition is developed in terms of linear matrix inequalities to determine the mode-dependent parameter of the proposed quasi-sliding surface such that the stochastic admissibility with a prescribed H ∞ performance of the sliding mode dynamics is guaranteed. Furthermore, the sliding mode controller is designed to assure that the state trajectories of the system will be driven onto the quasi-sliding surface and remain in there afterward. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design algorithms.

scholarly journals Feedback Finite-Time Stabilization of Impulsive Linear Systems over Piecewise Quadratic Domains

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Jing Huang ◽  
Jianxing Li ◽  
Linshan Bu ◽  
Honglei Xu
Keyword(s):  
Finite Time ◽  
State Feedback ◽  
Linear Time ◽  
Feedback Stabilization ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Time Stability ◽  
Finite Time Stability ◽  
Time Varying Systems

This paper investigates the state feedback stabilization problem for a class of impulsive linear time-varying systems over specified time intervals and piecewise quadratic domains (PQDs). First, concepts related to finite-time stability and PQDs are given. Second, finite-time stability analysis over PQDs is implemented, and a variety of stability conditions involving differential linear matrix inequalities are investigated. Then, computationally tractable stability conditions are established for the control design. Finally, an illustrative example is presented to show the effectiveness of the designed state feedback control.

State feedback control for stochastic Markovian jump delay systems based on LaSalle-type theorem

2018 ◽  
Vol 355 (5) ◽  
pp. 2179-2196 ◽  
Author(s):  
Guangming Zhuang ◽  
Jianwei Xia ◽  
Weihai Zhang ◽  
Junsheng Zhao ◽  
Qun Sun ◽  
...  
Keyword(s):  
Feedback Control ◽  
State Feedback ◽  
Type Theorem ◽  
State Feedback Control ◽  
Delay Systems ◽  
Markovian Jump ◽  
Markovian Jump Delay Systems

STATE-FEEDBACK CONTROL OF DISCRETE-TIME STOCHASTIC LINEAR SYSTEMS WITH MARKOVIAN SWITCHING

2020 ◽  
Vol 65 (6) ◽  
pp. 13-22
Author(s):  
Dung Nguyen Trung ◽  
Thu Tran Thi
Keyword(s):  
Feedback Control ◽  
Discrete Time ◽  
State Feedback ◽  
Transition Probabilities ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Discrete Time Markov Chain ◽  
Multiplicative Noises ◽  
Stochastic Linear Systems

This paper is concerned with the stabilization problem via state-feedback control of discrete-time jumping systems with stochastic multiplicative noises. The jumping process of the system is driven by a discrete-time Markov chain with finite states and partially known transition probabilities. Sufficient conditions are established in terms of tractable linear matrix inequalities to design a mode-dependent stabilizing state-feedback controller. A numerical example is provided to validate the effectiveness of the obtained result.

Robust Absolute Stabilization of Time-Varying Delay Systems with Maximum Admissible Perturbed Bound

2010 ◽  
Vol 40-41 ◽  
pp. 103-110
Author(s):  
Jie Jin
Keyword(s):  
State Feedback ◽  
State Feedback Control ◽  
Delay Systems ◽  
Linear Matrix ◽  
Control Law ◽  
Time Varying ◽  
Time Varying Delay ◽  
Linear State ◽  
Varying Delay ◽  
Nonlinear Delay

This paper is concerned the problem of robust absolute stabilization of time-varying delay systems with admissible perturbation in terms of integral inequality. A linear state-feedback control law is derived for one class of delay systems with sector restriction based on linear matrix inequality (LMI). Especially, this method does not require input terms are absolutely controllable for nonlinear delay systems. Numerical example is used to demonstrate the validity of the proposed method.

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