scholarly journals Finite-Time Stabilization for Stochastic Interval Systems with Time Delay and Application to Energy-Storing Electrical Circuits

Electronics ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 175 ◽  
Author(s):  
Guici Chen ◽  
Fei Wei ◽  
Wenbo Wang
Keyword(s):  
Delay Interval ◽  
Finite Time ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Electrical Circuit ◽  
Linear Matrix ◽  
Stochastic Delay ◽  
Finite Time Stabilization ◽  
Interval Systems ◽  
Nonlinear State

In this paper, the problem of stochastic finite-time stabilization is investigated for stochastic delay interval systems. A nonlinear state feedback controller with input-to-state delay is introduced. By employing the Lyapunov–Krasovskii functional method, some sufficient conditions on stochastic finite-time stabilization are derived for closed-loop stochastic delay interval systems using the I t o ^ ’s differential formula. Suitable nonlinear state feedback controllers can be designed in terms of linear matrix inequalities. The obtained results are finally applied to an energy-storing electrical circuit to illustrate the effectiveness of the proposed method.

Stochastic Finite-Time Stabilization for Uncertain Jump Systems via State Feedback

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
Shuping He ◽  
Fei Liu
Keyword(s):  
Finite Time ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Markov Jump ◽  
External Disturbances ◽  
Markov Jump Systems ◽  
Finite State ◽  
Finite Time Stabilization ◽  
Jump Systems

The stochastic finite-time stabilization problem is considered for a class of linear uncertain Markov jump systems that possess randomly jumping parameters. The transition of the jumping parameters is governed by a finite-state Markov process. By using the appropriate stochastic Lyapunov–Krasovskii functional approach, sufficient conditions are proposed for the design of stochastic finite-time stabilization controller. The stabilization criteria are formulated in the form of linear matrix inequalities and the designed finite-time stabilization controller is described as an optimization one. The designed finite-time stabilized controller makes the stochastic MJSs stochastic finite-time bounded and stochastic finite-time stabilizable for all admissible unknown external disturbances and uncertain parameters. Simulation results illustrate the effectiveness of the developed approaches.

Guaranteed cost and finite-time event-triggered control of fractional-order switched systems

2021 ◽  
pp. 014233122110048
Author(s):  
Yilin Shang ◽  
Leipo Liu ◽  
Yifan Di ◽  
Zhumu Fu ◽  
Bo Fan
Keyword(s):  
Fractional Order ◽  
Finite Time ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Electrical Circuit ◽  
Linear Matrix ◽  
Current State ◽  
Guaranteed Cost ◽  
Event Triggered

This paper considers the problem of guaranteed cost and finite-time event-triggered control of fractional-order switched systems. Firstly, an event-triggered scheme including both the information of current state and an exponential decay function is proposed, and a novel cost function that adopts the characteristics of fractional-order integration is presented. Secondly, some sufficient conditions are derived to guarantee that the corresponding closed-loop system is finite-time stable with a certain cost upper bound, using multiple Lyapunov functions and average dwell time approach. Meanwhile, the event-triggered parameters and state feedback gains are simultaneously obtained via solving linear matrix inequalities. Moreover, Zeno behavior does not exist by finding a positive lower bound of the triggered interval. Finally, an example about fractional-order switched electrical circuit is provided to show the effectiveness of the proposed method.

scholarly journals Finite-Time Stabilization for Stochastic Inertial Neural Networks with Time-Delay via Nonlinear Delay Controller

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Deyi Li ◽  
Yuanyuan Wang ◽  
Guici Chen ◽  
Shasha Zhu
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Finite Time ◽  
Design Method ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Nonlinear Feedback ◽  
Inertial Neural Networks ◽  
Finite Time Stabilization

This paper pays close attention to the problem of finite-time stabilization related to stochastic inertial neural networks with or without time-delay. By establishing proper Lyapunov-Krasovskii functional and making use of matrix inequalities, some sufficient conditions on finite-time stabilization are obtained and the stochastic settling-time function is also estimated. Furthermore, in order to achieve the finite-time stabilization, both delayed and nondelayed nonlinear feedback controllers are designed, respectively, in terms of solutions to a set of linear matrix inequalities (LMIs). Finally, a numerical example is provided to demonstrate the correction of the theoretical results and the effectiveness of the proposed control design method.

scholarly journals Finite-time stabilization of switched linear systems and its application in terminal guidance

2016 ◽  
Vol 13 (6) ◽  
pp. 172988141667980
Author(s):  
Yang Guo ◽  
Xiaoxiang Hu ◽  
Biao Deng ◽  
Shuai Zhang ◽  
Yu Jiang
Keyword(s):  
Linear Systems ◽  
Finite Time ◽  
State Feedback ◽  
State Constraints ◽  
Initial Conditions ◽  
Sufficient Conditions ◽  
Switched Linear Systems ◽  
Finite Time Stabilization ◽  
Finite Time Boundedness ◽  
Terminal Guidance

This article presents finite-time stabilization methods of switched linear systems with disturbances. After extending finite-time stabilization and finite-time boundedness definitions to switched linear systems, sufficient conditions guaranteeing system finite-time boundedness are proposed, by which the state feedback controller method is obtained. For a class of switched terminal guidance systems, the methods are illustrated by application to guidance design to solve the finite-time stabilization problem considering nonzero initial conditions and state constraints.

scholarly journals Finite-Time Robust Stabilization for Stochastic Neural Networks

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Weixiong Jin ◽  
Xiaoyang Liu ◽  
Xiangjun Zhao ◽  
Nan Jiang ◽  
Zhengxin Wang
Keyword(s):  
Neural Networks ◽  
Finite Time ◽  
Robust Stabilization ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Stochastic Nonlinear Systems ◽  
Stochastic Neural Networks ◽  
Time Stability ◽  
Finite Time Stability ◽  
Finite Time Stabilization

This paper is concerned with the finite-time stabilization for a class of stochastic neural networks (SNNs) with noise perturbations. The purpose of the addressed problem is to design a nonlinear stabilizator which can stabilize the states of neural networks in finite time. Compared with the previous references, a continuous stabilizator is designed to realize such stabilization objective. Based on the recent finite-time stability theorem of stochastic nonlinear systems, sufficient conditions are established for ensuring the finite-time stability of the dynamics of SNNs in probability. Then, the gain parameters of the finite-time controller could be obtained by solving a linear matrix inequality and the robust finite-time stabilization could also be guaranteed for SNNs with uncertain parameters. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design method.

scholarly journals Neural Network Based Finite-Time Stabilization for Discrete-Time Markov Jump Nonlinear Systems with Time Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Fei Chen ◽  
Fei Liu ◽  
Hamid Reza Karimi
Keyword(s):  
Neural Networks ◽  
Nonlinear Systems ◽  
Discrete Time ◽  
Finite Time ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Space Representation ◽  
Linear Matrix ◽  
Markov Jump ◽  
Finite Time Stabilization

This paper deals with the finite-time stabilization problem for discrete-time Markov jump nonlinear systems with time delays and norm-bounded exogenous disturbance. The nonlinearities in different jump modes are parameterized by neural networks. Subsequently, a linear difference inclusion state space representation for a class of neural networks is established. Based on this, sufficient conditions are derived in terms of linear matrix inequalities to guarantee stochastic finite-time boundedness and stochastic finite-time stabilization of the closed-loop system. A numerical example is illustrated to verify the efficiency of the proposed technique.

scholarly journals Observer-Based Finite-TimeH∞Control of Singular Markovian Jump Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Yingqi Zhang ◽  
Wei Cheng ◽  
Xiaowu Mu ◽  
Xiulan Guo
Keyword(s):  
Finite Time ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Markovian Jump Systems ◽  
Feasibility Problem ◽  
Auxiliary Result ◽  
Markovian Jump ◽  
Singular Markovian Jump Systems ◽  
Finite Time Stabilization ◽  
Jump Systems

This paper addresses the problem of finite-timeH∞control via observer-based state feedback for a family of singular Markovian jump systems (SMJSs) with time-varying norm-bounded disturbance. Firstly, the concepts of singular stochastic finite-time boundedness and singular stochastic finite-timeH∞stabilization via observer-based state feedback are given. Then an observer-based state feedback controller is designed to ensure singular stochastic finite-timeH∞stabilization via observer-based state feedback of the resulting closed-loop error dynamic SMJS. Sufficient criteria are presented for the solvability of the problem, which can be reduced to a feasibility problem involving linear matrix inequalities with a fixed parameter. As an auxiliary result, we also discuss the problem of finite-time stabilization via observer-based state feedback of a class of SMJSs and give sufficient conditions of singular stochastic finite-time stabilization via observer-based state feedback for the class of SMJSs. Finally, illustrative examples are given to demonstrate the validity of the proposed techniques.

scholarly journals Finite-time stabilization of switched nonlinear singular systems with asynchronous switching

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jing Wang ◽  
Xingtao Wang
Keyword(s):  
Finite Time ◽  
Singular Systems ◽  
Singular System ◽  
Sufficient Conditions ◽  
Original System ◽  
Linear Matrix ◽  
Finite Time Stability ◽  
Nonlinear Singular Systems ◽  
Time Period ◽  
Finite Time Stabilization

AbstractThis paper is concerned with the finite-time stabilization of a class of switched nonlinear singular systems under asynchronous control. Asynchronism here refers to the delays in switching between the controller and the subsystem. First, the dynamic decomposition technique is used to prove that such a switched singular system is regular and impulse-free. Secondly, based on the state solutions of the closed-loop system in the matched time period and the mismatched time period of the system instead of constructing a Lyapunov function, the sufficient conditions for the finite-time stability of the asynchronous switched singular system are given, there is no limit to the stability of subsystems. Then, the mode-dependent state feedback controller that makes the original system stable is derived in the form of strict linear matrix inequalities. Finally, numerical examples are given to verify the feasibility and validity of the results.

scholarly journals Finite-Time Stability and Stabilization of Nonlinear Quadratic Systems with Jumps

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Minsong Zhang
Keyword(s):  
Finite Time ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Time Stability ◽  
Quadratic Systems ◽  
Finite Time Stability ◽  
Jump Time ◽  
Stability And Stabilization ◽  
Finite Time Stabilization

This paper investigates the problems of finite-time stability and finite-time stabilization for nonlinear quadratic systems with jumps. The jump time sequences here are assumed to satisfy some given constraints. Based on Lyapunov function and a particular presentation of the quadratic terms, sufficient conditions for finite-time stability and finite-time stabilization are developed to a set containing bilinear matrix inequalities (BLIMs) and linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the proposed methodology.

scholarly journals Time-Varying Delayed H∞ Control Problem for Nonlinear Systems: A Finite Time Study Using Quadratic Convex Approach

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 713 ◽  
Author(s):  
Chanikan Emharuethai ◽  
Piyapong Niamsup ◽  
Raja Ramachandran ◽  
Wajaree Weera
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
State Feedback ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Finite Time Boundedness ◽  
Varying Delay

In this manuscript, we consider the finite-time H ∞ control for nonlinear systems with time-varying delay. With the assistance of a novel Lyapunov-Krasovskii functional which includes some integral terms, a matrix-based on quadratic convex approach, combined with Wirtinger inequalities and some useful integral inequalities, a sufficient condition of finite-time boundedness is established. A novel feature presents in this paper is that the restriction which is necessary for the upper bound derivative is not restricted to less than 1. Further a H ∞ controller is designed via memoryless state feedback control and a new sufficient conditions for the existence of finite-time H ∞ state feedback for the system are given in terms of linear matrix inequalities (LMIs). At the end, some numerical examples with simulations are given to illustrate the effectiveness of the obtained result.

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