Delay Dependent Robust Stabilization for Systems With Uncertain Time Varying Delays

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
El Houssaine Tissir
Keyword(s):  
Time Derivative ◽  
Robust Stabilization ◽  
Uncertain System ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Time Varying ◽  
Stability Robustness ◽  
Improved Stability ◽  
Uncertain Time ◽  
Delay Dependent

Sufficient and improved stability robustness conditions that depend both on the size and time derivative of time varying delays are presented. The approach is applied to investigate the problem of finding memoryless state feedback control that simultaneously stabilizes the uncertain system and guarantees an upper bound for some performance index. The perturbations are unknown but norm bounded. The results are derived via Lyapunov– Krasovskii functional and are expressed in terms of linear matrix inequalities. Numerical computations are performed to illustrate the feasibility and the improvements of the results with respect to previous works.

scholarly journals Improved Stability Criteria of Static Recurrent Neural Networks with a Time-Varying Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Lei Ding ◽  
Hong-Bing Zeng ◽  
Wei Wang ◽  
Fei Yu
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Improved Stability ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper investigates the stability of static recurrent neural networks (SRNNs) with a time-varying delay. Based on the complete delay-decomposing approach and quadratic separation framework, a novel Lyapunov-Krasovskii functional is constructed. By employing a reciprocally convex technique to consider the relationship between the time-varying delay and its varying interval, some improved delay-dependent stability conditions are presented in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to show the merits and the effectiveness of the proposed methods.

scholarly journals Robust Moving HorizonH∞Control of Discrete Time-Delayed Systems with Interval Time-Varying Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
F. Yıldız Tascikaraoglu ◽  
I. B. Kucukdemiral ◽  
J. Imura
Keyword(s):  
Discrete Time ◽  
Disturbance Rejection ◽  
Closed Loop ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Time Varying ◽  
Discrete Time System ◽  
Delayed Systems ◽  
State Delays ◽  
Delay Dependent

In this study, design of a delay-dependent type moving horizon state-feedback control (MHHC) is considered for a class of linear discrete-time system subject to time-varying state delays, norm-bounded uncertainties, and disturbances with bounded energies. The closed-loop robust stability and robust performance problems are considered to overcome the instability and poor disturbance rejection performance due to the existence of parametric uncertainties and time-delay appeared in the system dynamics. Utilizing a discrete-time Lyapunov-Krasovskii functional, some delay-dependent linear matrix inequality (LMI) based conditions are provided. It is shown that if one can find a feasible solution set for these LMI conditions iteratively at each step of run-time, then we can construct a control law which guarantees the closed-loop asymptotic stability, maximum disturbance rejection performance, and closed-loop dissipativity in view of the actuator limitations. Two numerical examples with simulations on a nominal and uncertain discrete-time, time-delayed systems, are presented at the end, in order to demonstrate the efficiency of the proposed method.

scholarly journals Improved Stability Criteria for Markovian Jump Systems with Time-Varying Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Yu-cai Ding ◽  
Hui Liu ◽  
Baodan Tian
Keyword(s):  
Convex Combination ◽  
Markovian Jump Systems ◽  
Combination Method ◽  
Linear Matrix ◽  
Time Varying ◽  
Markovian Jump ◽  
Improved Stability ◽  
Lyapunov Matrix ◽  
Delay Dependent ◽  
Jump Systems

The delay-dependent stochastic stability problem of Markovian jump systems with time-varying delays is investigated in this paper. Though the Lyapunov-Krasovskii functional is general and simple, less conservative results are derived by using the convex combination method, improved Wirtinger’s integral inequality, and a slack condition on Lyapunov matrix. The obtained results are formulated in terms of linear matrix inequalities (LMIs). Numerical examples are provided to verify the effectiveness and superiority of the presented results.

scholarly journals Stability and Stabilization for Polytopic LPV Systems with Parameter-Varying Time Delays

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Fu Chen ◽  
Shugui Kang ◽  
Fangyuan Li
Keyword(s):  
Time Delays ◽  
Time Derivative ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Lpv Systems ◽  
Stability And Stabilization ◽  
Parameter Varying ◽  
Conditions Of Stability ◽  
Delay Dependent

In this paper, we deal with the problem of stability and stabilization for linear parameter-varying (LPV) systems with time-varying time delays. The uncertain parameters are assumed to reside in a polytope with bounded variation rates. Being main difference from the existing achievements, the representation of the time derivative of the time-varying parameter is under a polytopic structure. Based on the new representation, delay-dependent sufficient conditions of stability and stabilization are, respectively, formulated in terms of linear matrix inequalities (LMI). Simulation examples are then provided to confirm the effectiveness of the given approach.

scholarly journals Improved Delay-Dependent Stability Analysis for Neural Networks with Interval Time-Varying Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Jun-kang Tian ◽  
Yan-min Liu
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Upper And Lower Bounds ◽  
Linear Matrix ◽  
Time Varying ◽  
Interval Time ◽  
Time Varying Delay ◽  
Improved Stability ◽  
Delay Dependent ◽  
Delay Partitioning

The problem of delay-dependent asymptotic stability analysis for neural networks with interval time-varying delays is considered based on the delay-partitioning method. Some less conservative stability criteria are established in terms of linear matrix inequalities (LMIs) by constructing a new Lyapunov-Krasovskii functional (LKF) in each subinterval and combining with reciprocally convex approach. Moreover, our criteria depend on both the upper and lower bounds on time-varying delay and its derivative, which is different from some existing ones. Finally, a numerical example is given to show the improved stability region of the proposed results.

Improved Stability Analysis for Neural Networks with Interval Time-Varying Delays

2014 ◽  
Vol 687-691 ◽  
pp. 2078-2082 ◽  
Author(s):  
Ze Rong Ren ◽  
Jun Kang Tian
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Upper And Lower Bounds ◽  
Linear Matrix ◽  
Time Varying ◽  
Interval Time ◽  
Time Varying Delay ◽  
Improved Stability ◽  
Delay Dependent ◽  
Delay Partitioning

In this paper, the problem of delay-dependent asymptotic stability analysis for neural networks with interval time-varying delays is considered. By the use of delay-partitioning method and some novel techniques, some less conservative stability criteria are established in terms of linear matrix inequalities. Moreover, our criteria depend on both the upper and lower bounds of time-varying delay and its derivative, which is different from some existing ones. Finally, an numerical example is given to show the improved stability region of the proposed results.

scholarly journals Stability of Teleoperation Systems for Time-Varying Delays by Neutral LMI Techniques

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Emma Delgado ◽  
Miguel Díaz-Cacho ◽  
Antonio Barreiro
Keyword(s):  
Time Derivative ◽  
Neutral Type ◽  
The State ◽  
Stable Region ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
And Performance ◽  
Channel Control ◽  
Delay Dependent

This paper investigates the delay-dependent stability of a teleoperation system based on the transparent Generalized Four-Channel control (G-4C) scheme under time-varying communication delays. To address stability we choose here a primitive result providing a Linear Matrix Inequalities (LMIs) approach based on Lyapunov-Krasovskii functionals. Firstly, the scheme is modeled as the neutral-type differential-delayed equation; that is, the delay affects not only the state but also the state derivative. Secondly, we apply a less conservative stability criteria based on LMIs that are delay dependent and delay's time-derivative dependent. The reason is that, for better performance in the case of small delays, we must accept the possibility that stability is lost for large delays. The approach is applied to an example, and its advantages are discussed. As a result, we propose to modify the values of standard controllers in G-4C defining theμ-4C scheme, which introduces a tuning factorμto increase in practical conditions the stable region fixing the desired bounds on time-varying delay, with the particularity of maintaining the tracking properties provided by this transparent control scheme. The simulation results justify the proposed control architecture and confirm robust stability and performance.

scholarly journals Novel Stabilization Conditions for Uncertain Singular Systems with Time-Varying Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Yuanchun Ding ◽  
Falu Weng ◽  
Ji Ge ◽  
Qi Liang ◽  
Xueyi Zhi
Keyword(s):  
Singular Systems ◽  
Singular System ◽  
Robust Stabilization ◽  
State Feedback Control ◽  
Delay Systems ◽  
Time Varying ◽  
Time Varying Delay ◽  
Uncertain Singular Systems ◽  
Delay Dependent ◽  
Varying Delay

The problem of delay-dependent robust stabilization for continuously singular time-varying delay systems with norm-bounded uncertainties is investigated in this paper. First, based on some mathematical transform, the uncertain singular system is described in a form which involves the time-delay integral items. Then, in terms of the delay-range-dependent Lyapunov functional and the LMI technique, the improved delay-dependent LMIs-based conditions are established for the uncertain singular systems with time-varying delay to be regular, causal, and stable. Furthermore, by solving these LMIs, an explicit expression for the desired state feedback control law can be obtained; thus, the regularity, causality, and stability of the closed-loop system are guaranteed. In the end, numerical examples are given to illustrate the effectiveness of the proposed methods.

scholarly journals Global Dissipativity on Uncertain Discrete-Time Neural Networks with Time-Varying Delays

2010 ◽  
Vol 2010 ◽  
pp. 1-19 ◽  
Author(s):  
Qiankun Song ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Discrete Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Computationally Efficient ◽  
Inequality Technique ◽  
General Activation ◽  
Delay Dependent

The problems on global dissipativity and global exponential dissipativity are investigated for uncertain discrete-time neural networks with time-varying delays and general activation functions. By constructing appropriate Lyapunov-Krasovskii functionals and employing linear matrix inequality technique, several new delay-dependent criteria for checking the global dissipativity and global exponential dissipativity of the addressed neural networks are established in linear matrix inequality (LMI), which can be checked numerically using the effective LMI toolbox in MATLAB. Illustrated examples are given to show the effectiveness of the proposed criteria. It is noteworthy that because neither model transformation nor free-weighting matrices are employed to deal with cross terms in the derivation of the dissipativity criteria, the obtained results are less conservative and more computationally efficient.

scholarly journals Convex Polyhedron Method to Stability of Continuous Systems with Two Additive Time-Varying Delay Components

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Tiejun Li ◽  
Junkang Tian
Keyword(s):  
Stability Criterion ◽  
Convex Polyhedron ◽  
Linear Matrix ◽  
Continuous Systems ◽  
Time Varying ◽  
Time Varying Delay ◽  
Polyhedron Method ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper is concerned with delay-dependent stability for continuous systems with two additive time-varying delay components. By constructing a new class of Lyapunov functional and using a new convex polyhedron method, a new delay-dependent stability criterion is derived in terms of linear matrix inequalities. The obtained stability criterion is less conservative than some existing ones. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.

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