scholarly journals H∞Observer-Based Sliding Mode Control for Uncertain Stochastic Systems with Time-Varying Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Peng Zhang ◽  
Yonggui Kao ◽  
Jingyan Zhu ◽  
Wei Li
Keyword(s):  
Sliding Mode Control ◽  
Stochastic Systems ◽  
Sliding Mode ◽  
Sufficient Conditions ◽  
Disturbance Attenuation ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Interval ◽  
Stochastic Perturbations ◽  
Mode Control

The paper is concerned with sliding mode control for uncertain time-delay systems subjected to input nonlinearity and stochastic perturbations. Using the sliding mode control, a robust law is derived to guarantee the reachability of the sliding surface in a finite time interval. The sufficient conditions on asymptotic stability of the error system and sliding mode dynamics with disturbance attenuation level are presented in terms of linear matrix inequalities (LMIs). Finally, an example is provided to illustrate the efficiency and effectiveness of the proposed method.

Sliding Mode Control Based on Novel Nonlinear Sliding Surface for a Class of Time-Varying Delay Systems

2014 ◽  
Vol 615 ◽  
pp. 375-381
Author(s):  
Qi Feng Ren ◽  
Cun Che Gao ◽  
Shu Hui Bi
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Sliding Surface ◽  
Time Varying Delay ◽  
Mode Control ◽  
Varying Delay

The sliding mode control (SMC) design is discussed for a class of time-varying delay systems which is delay-range-dependent and rate-range-dependent. A novel time-varying nonlinear sliding surface is employed. The choice of nonlinear sliding surface is to change the state matrix of sliding mode system, which can combine the advantages of different conventional linear sliding surfaces. Thus the better transient qualities of system states, i.e., quicker response and smaller overshoot, can be achieved. The sufficient conditions ensuring the asymptotic stability of sliding mode are derived in terms of linear matrix inequalities. The algorithms deciding unknown parameters of the nonlinear sliding surface and the corresponding sliding mode controller are also presented. Finally, A numerical example is given to illustrate the effectiveness of the result here.

scholarly journals Adaptive Output Feedback Sliding Mode Control for Complex Interconnected Time-Delay Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-15
Author(s):  
Van Van Huynh ◽  
Yao-Wen Tsai ◽  
Phan Van Duc
Keyword(s):  
Time Delay ◽  
Sliding Mode Control ◽  
Output Feedback ◽  
Sliding Mode ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Order System ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Mode Control

We extend the decentralized output feedback sliding mode control (SMC) scheme to stabilize a class of complex interconnected time-delay systems. First, sufficient conditions in terms of linear matrix inequalities are derived such that the equivalent reduced-order system in the sliding mode is asymptotically stable. Second, based on a new lemma, a decentralized adaptive sliding mode controller is designed to guarantee the finite time reachability of the system states by using output feedback only. The advantage of the proposed method is that two major assumptions, which are required in most existing SMC approaches, are both released. These assumptions are (1) disturbances are bounded by a known function of outputs and (2) the sliding matrix satisfies a matrix equation that guarantees the sliding mode. Finally, a numerical example is used to demonstrate the efficacy of the method.

scholarly journals Sliding Mode Control of Uncertain Neutral Stochastic Systems with Multiple Delays

2008 ◽  
Vol 2008 ◽  
pp. 1-9 ◽  
Author(s):  
Dilan Chen ◽  
Weidong Zhang
Keyword(s):  
Sliding Mode Control ◽  
Stochastic Systems ◽  
Sliding Mode ◽  
Linear Matrix ◽  
Multiple Delays ◽  
Sliding Mode Controller ◽  
Matrix Inequalities ◽  
Neutral Systems ◽  
Mode Control ◽  
Neutral Stochastic Systems

This paper is concerned with the sliding mode control for uncertain stochastic neutral systems with multiple delays. A switching surface is adopted first. Then, by means of linear matrix inequalities (LMIs), a sufficient condition is derived to ensure the global stochastic stability of the stochastic system in the sliding mode for all admissible uncertainties. The synthesized sliding mode controller guarantees the existence of the sliding mode.

New results on robust sliding mode control for linear time-delay systems

2020 ◽  
Author(s):  
Jothiappan Palraj ◽  
Kalidass Mathiyalagan ◽  
Peng Shi
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Linear Time ◽  
Lyapunov Stability Theory ◽  
Delay Systems ◽  
Linear Matrix ◽  
Switching Surface ◽  
Mode Control ◽  
Short Time ◽  
Robust Asymptotic Stability

Abstract This work focuses on the sliding mode control (SMC) for a family of linear systems with uncertainties and time-varying delays. First, an integral switching surface is constructed to verify the robust asymptotic stability of the considered system and the results are extended to analyse the mixed $\mathscr{H}_{\infty }\big /$Passivity performance index. Thereafter, a suitable SMC law is developed to force the system state onto the predefined switching surface in short time. By using Lyapunov stability theory, some novel results are obtained, and the required stability conditions are established in terms of linear matrix inequalities which can be solved by standard Matlab toolbox. Finally, the results are validated over a Chua’s circuit model, which describes the practical application of the developed results.

Finite-time H∞ sliding mode control of uncertain T-S fuzzy system with time-varying delay based on observer

2021 ◽  
Vol 40 (1) ◽  
pp. 983-999
Author(s):  
Huan Li ◽  
Pengyi Tang ◽  
Yuechao Ma
Keyword(s):  
Sliding Mode Control ◽  
Finite Time ◽  
Sliding Mode ◽  
Linear Matrix ◽  
Time Interval ◽  
Sliding Mode Controller ◽  
Time Varying ◽  
Sliding Surface ◽  
State Estimator ◽  
Mode Control

In this paper, a class of observer-based sliding mode controller is designed, and the finite-time H∞ control problem of uncertain T-S fuzzy systems with time-varying is studied. Firstly, an integral-type sliding surface function with time-delay is devised based on the state estimator, and sufficient criteria of finite-time bounded and finite-time H∞ bounded can be obtained for the T-S systems. Moreover, the proposed sliding mode control law is integrated to ensure the dynamics of controlled system into the sliding surface in a finite-time interval. Then, according to the linear matrix inequalities (LMIs), the desired gain matrices of fuzzy sliding mode controller and state estimator are derived. Finally, effectiveness gives some illustrative examples may be used to display the value of the current proposed method as well as a significant improvement.

Linear matrix inequalities design approach for robust stabilization of uncertain nonlinear systems with perturbation based on optimally-tuned global sliding mode control

2015 ◽  
Vol 23 (8) ◽  
pp. 1285-1295 ◽  
Author(s):  
Saleh Mobayen ◽  
Dumitru Baleanu
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Search Algorithm ◽  
Random Search ◽  
Robust Stabilization ◽  
Sufficient Conditions ◽  
Control Technique ◽  
Linear Matrix ◽  
Mode Control ◽  
Global Sliding Mode Control

This paper presents a novel global sliding mode control technique for the stabilization of a class of uncertain and nonlinear dynamic systems with perturbation. Using the Lyapunov stability theory and linear matrix inequality, some sufficient conditions are deduced to guarantee the asymptotic stabilization of the system states and to modify the robustness of the system. To improve the robust performance, an innovative reaching control law is designed to guarantee a chattering-free finite time performance under the uncertainty and nonlinearities and is optimally tuned using a modified random search algorithm. Simulation results are provided to show the effectiveness of the suggested technique.

scholarly journals H∞ Robust T-S Fuzzy Design for Uncertain Nonlinear Systems with State Delays Based on Sliding Mode Control

2010 ◽  
Vol 5 (4) ◽  
pp. 592 ◽  
Author(s):  
Xizheng Zhang ◽  
Yaonan Wang ◽  
Xiaofang Yuan
Keyword(s):  
Nonlinear Systems ◽  
Sliding Mode Control ◽  
Sliding Mode ◽  
External Disturbance ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Parameter Uncertainties ◽  
Mode Control ◽  
Disturbance Attenuation Level ◽  
Takagi Sugeno

This paper presents the fuzzy design of sliding mode control (SMC) for nonlinear systems with state delay, which can be represented by a Takagi-Sugeno (TS) model with uncertainties. There exist the parameter uncertainties in both the state and input matrices, as well as the unmatched external disturbance. The key feature of this work is the integration of SMC method with H∞ technique such that the robust asymptotically stability with a prescribed disturbance attenuation level γ can be achieved. A sufficient condition for the existence of the desired SMC is obtained by solving a set of linear matrix inequalities (LMIs). The reachability of the specified switching surface is proven. Simulation results show the validity of the proposed method.

Robust Observer-Based Finite Time Sliding Mode Control for One-Sided Lipschitz Systems With Uncertainties

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Junchao Ren ◽  
Jie Sun ◽  
Fangfang Li
Keyword(s):  
Sliding Mode Control ◽  
Finite Time ◽  
Closed Loop ◽  
Sliding Mode ◽  
Sufficient Conditions ◽  
Time Interval ◽  
Parameter Uncertainties ◽  
Robust Observer ◽  
Mode Control ◽  
Finite Time Boundedness

Abstract This paper investigates the problem of observer-based finite time sliding mode control (SMC) for a class of one-sided Lipschitz (OSL) systems with uncertainties. The parameter uncertainties are assumed to be time-varying norm-bounded appearing not only in both the state and output matrices but also in the nonlinear function. For a time interval [0,T], we divide it into two parts: one part is the reaching phase within [0,T*] and another part is the sliding motion phase within [T*,T]. First, the reachability of the sliding mode surface with T*≤T is proved. Next, several conditions are proposed which ensure robust finite time boundedness (FTB) of the corresponding closed-loop systems in the interval [0,T*] and [T*,T], respectively. Then, the sufficient conditions, which guarantee robust finite time boundedness of the closed-loop system in whole time interval [0,T], are given in terms of linear matrix inequalities (LMIs), and further the robust observer and controller can be designed in an LMI frame. A convex optimization problem subject to LMIs is formulated to optimize the desired performance indices of interest to us. Finally, a practical example is given to demonstrate the effectiveness of the proposed methods.

Neural Adaptive Sliding Mode Control for a Class of Nonlinear Neutral Delay Systems

2008 ◽  
Vol 130 (6) ◽  
Author(s):  
Yugang Niu ◽  
James Lam ◽  
Xingyu Wang ◽  
Daniel W. C. Ho
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Delay System ◽  
Delay Systems ◽  
Adaptive Sliding Mode Control ◽  
Linear Matrix ◽  
Sliding Surface ◽  
Neutral Delay ◽  
Neutral Delay Systems ◽  
Mode Control

This paper is concerned with the problem of sliding mode control (SMC) for a class of neutral delay systems with unknown nonlinear uncertainties that may not satisfy the norm-bounded condition. A SMC scheme based on neural-network approximation is proposed for the uncertain neutral delay system. By means of linear matrix inequality (LMI) approach, a sufficient condition is given such that the resultant closed-loop system is guaranteed to be stable, and the states asymptotically converge to zero. When the LMI is feasible, the designs of both the sliding surface and the sliding mode control law can be easily obtained via convex optimization. It is shown that the state trajectories are driven toward the specified sliding surface that depends on the current states as well as the delayed states. Finally, a simulation result is given to illustrate the effectiveness of the proposed method.

Discrete T–S fuzzy systems with time-varying delays: a new discrete sliding mode control approach

2017 ◽  
Vol 40 (7) ◽  
pp. 2332-2339 ◽  
Author(s):  
Yassine Ben Yazid ◽  
Driss Mehdi ◽  
Ahmed Said Nouri
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Delay Systems ◽  
Linear Matrix ◽  
Control Input ◽  
Common Input ◽  
Restrictive Assumption ◽  
Control Approach ◽  
Mode Control ◽  
Discrete Sliding Mode Control

The control of nonlinear systems has been the subject of extensive research. This interest is mainly due to its potential for real applications. In this paper, we investigated discrete sliding mode control for a class of nonlinear time-delay systems represented by T–S fuzzy models. In most existing fuzzy sliding mode control, a common input matrix is considered for all subsystems. This assumption is very restrictive. Therefore, we proposed a new sliding surface, which takes account of the system state and the control input in order to exclude the restrictive assumption. Furthermore, we have improved the latter sliding mode control scheme, by adding delayed states. Based on formulation of linear matrix inequalities, the parameters of the sliding function are obtained. Therefore, to further reduce the conservatism in the existing results, the Wirtinger-based integral inequality and Jensens inequality are employed. To show the applicability and effectiveness of the proposed controller design methodology, a numerical example is given for illustration.

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