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.

A DELAY-DEPENDENT APPROACH TO ROBUST TAKAGI–SUGENO FUZZY CONTROL OF UNCERTAIN RECURRENT NEURAL NETWORKS WITH MIXED INTERVAL TIME-VARYING DELAYS

2011 ◽  
Vol 20 (08) ◽  
pp. 1571-1589 ◽  
Author(s):  
K. H. TSENG ◽  
J. S. H. TSAI ◽  
C. Y. LU
Keyword(s):  
Fuzzy Control ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Upper And Lower Bounds ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Time Varying ◽  
Interval Time ◽  
Delay Dependent ◽  
Takagi Sugeno

This paper deals with the problem of globally delay-dependent robust stabilization for Takagi–Sugeno (T–S) fuzzy neural network with time delays and uncertain parameters. The time delays comprise discrete and distributed interval time-varying delays and the uncertain parameters are norm-bounded. Based on Lyapunov–Krasovskii functional approach and linear matrix inequality technique, delay-dependent sufficient conditions are derived for ensuring the exponential stability for the closed-loop fuzzy control system. An important feature of the result is that all the stability conditions are dependent on the upper and lower bounds of the delays, which is made possible by using the proposed techniques for achieving delay dependence. Another feature of the results lies in that involves fewer matrix variables. Two illustrative examples are exploited in order to illustrate the effectiveness of the proposed design methods.

scholarly journals Robust Stability and Stabilization of a Class of Uncertain Nonlinear Discrete-Time Stochastic Systems with Interval Time-Varying Delays

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Shuang Liang ◽  
Yali Dong
Keyword(s):  
Discrete Time ◽  
Stochastic Stability ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Interval Time ◽  
Stochastic Stabilization ◽  
Stability And Stabilization ◽  
Delay Dependent

This paper deals with the problems of the robust stochastic stability and stabilization for a class of uncertain discrete-time stochastic systems with interval time-varying delays and nonlinear disturbances. By utilizing a new Lyapunov-Krasovskii functional and some well-known inequalities, some new delay-dependent criteria are developed to guarantee the robust stochastic stability of a class of uncertain discrete-time stochastic systems in terms of the linear matrix inequality (LMI). Then based on the state feedback controller, the delay-dependent sufficient conditions of robust stochastic stabilization for a class of uncertain discrete-time stochastic systems with interval time-varying delays are established. The controller gain is designed to ensure the robust stochastic stability of the closed-loop system. Finally, illustrative examples are given to demonstrate the effectiveness of the proposed method.

scholarly journals Nonfragile H∞ Filter Design for Nonlinear Continuous-Time System with Interval Time-Varying Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-17
Author(s):  
Zhongda Lu ◽  
Guoliang Zhang ◽  
Yi Sun ◽  
Jie Sun ◽  
Fangming Jin ◽  
...  
Keyword(s):  
Continuous Time ◽  
Filter Design ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Decoupling Method ◽  
Interval Time ◽  
Time Varying Delay ◽  
Error System ◽  
Delay Dependent

This paper investigates nonfragile H∞ filter design for a class of continuous-time delayed Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delays. Filter parameters occur multiplicative gain variations according to the filter’s implementation, to handle this variations, a nonfragile H∞ filter is presented and a novel filtering error system is established. The nonfragile H∞ filter guarantees the filtering error system to be asymptotically stable and satisfies given H∞ performance index. By constructing a novel Lyapunov-Krasovskii function and using the linear matrix inequality (LMI), delay-dependent conditions are exploited to derive sufficient conditions for nonfragile designing H∞ filter. Using new matrix decoupling method to reduce the computational complexity, the filter parameters can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, numerical examples are given to show the effectiveness of the proposed method.

scholarly journals Stability and stabilizability of dynamical systems with multiple time-varying delays: delay-dependent criteria

2003 ◽  
Vol 2003 (4) ◽  
pp. 137-152 ◽  
Author(s):  
D. Mehdi ◽  
E. K. Boukas
Keyword(s):  
Time Delays ◽  
Uncertain Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Multiple Time ◽  
Multiple Time Delays ◽  
The Stability ◽  
Delay Dependent ◽  
Bounded Uncertainties ◽  
Norm Bounded Uncertainties

This paper deals with the class of uncertain systems with multiple time delays. The stability and stabilizability of this class of systems are considered. Their robustness are also studied when the norm-bounded uncertainties are considered. Linear matrix inequality (LMIs) delay-dependent sufficient conditions for both stability and stabilizability and their robustness are established to check if a system of this class is stable and/or is stabilizable. Some numerical examples are provided to show the usefulness of the proposed results.

State feedback observer-based control design for linear descriptor systems with multiple time-varying delays

2020 ◽  
Vol 37 (4) ◽  
pp. 1218-1236
Author(s):  
V N Phat ◽  
P Niamsup ◽  
N H Muoi
Keyword(s):  
State Feedback ◽  
Design Method ◽  
Sufficient Conditions ◽  
Descriptor Systems ◽  
Linear Matrix ◽  
Multiple Time ◽  
Time Varying ◽  
Feedback Controllers ◽  
Delay Function ◽  
Delay Dependent

Abstract In this paper, we propose an linear matrix inequality (LMI)-based design method to observer-based control problem of linear descriptor systems with multiple time-varying delays. The delay function can be continuous and bounded but not necessarily differentiable. First, by introducing a new set of improved Lyapunov–Krasovskii functionals that avoid calculating the derivative of the delay function, we obtain new delay-dependent sufficient conditions for guaranteeing the system to be regular, impulse-free and asymptotically stable. Then, based on the derived stability conditions, we design state feedback controllers and observer gains via LMIs, which can be solved numerically in standard computational algorithms. A numerical example with simulation is given to demonstrate the efficiency and validity of the proposed deign.

Delay-Dependent Robust Control for Discrete-Time Uncertain Stochastic Systems With Time-Varying Delays

2017 ◽  
Vol 139 (10) ◽  
Author(s):  
Cheung-Chieh Ku ◽  
Guan-Wei Chen
Keyword(s):  
Robust Control ◽  
Discrete Time ◽  
Stochastic Systems ◽  
Design Method ◽  
Sufficient Conditions ◽  
Jensen Inequality ◽  
Linear Matrix ◽  
Time Varying ◽  
Gain Scheduled Controller ◽  
Delay Dependent

This paper investigates a delay-dependent robust control problem of discrete-time uncertain stochastic systems with delays. The uncertainty considered in this paper is time-varying but norm-bounded, and the delays are considered as interval time-varying case for both state and input. According to the considerations of uncertainty, stochastic behavior, and time delays, the problem considered in this paper is more general than the existing works for uncertain stochastic systems. Via the proposed Lyapunov–Krasovskii function, some sufficient conditions are derived into the extended linear matrix inequality form. Moreover, Jensen inequality and free matrix equation are employed to reduce conservatism of those conditions. Through using the proposed design method, a gain-scheduled controller is designed to guarantee asymptotical stability of uncertain stochastic systems in the sense of mean square. Finally, two numerical examples are provided to demonstrate applicability and effectiveness of the proposed design method.

Delay-Dependent L1 Filtering for LPV Systems With Parameter-Varying Delays

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Yanhui Li ◽  
Yan Liang ◽  
Xionglin Luo
Keyword(s):  
Filter Design ◽  
Peak Performance ◽  
Linear Matrix ◽  
Compact Set ◽  
Worst Case ◽  
Lpv Systems ◽  
Error System ◽  
Parameter Varying ◽  
Space Data ◽  
Delay Dependent

The paper investigates the problems of delay-dependent L1 filtering for linear parameter-varying (LPV) systems with parameter-varying delays, in which the state-space data and the time delays are dependent on parameters that are measurable in real-time and vary in a compact set with bounded variation rate. The attention is focused on the design of L1 filter that guarantees the filtering error system to be asymptotically stable and satisfies the worst-case peak-to-peak gain of the filtering error system. In particular, we concentrate on the delay-dependent case, using parameter-dependent Lyapunov function, the decoupled peak-to-peak performance criterion is first established for a class of LPV systems. Under this condition, the admissible filter can be found in terms of linear matrix inequality (LMI) technology. According to approximate basis function and the gridding technique, the filter design problem is transformed into feasible solution problem of the finite parameter LMIs. Finally, a numerical example is provided to illustrate the feasibility of the developed approach.

Synchronization of Uncertain Neural Networks with H8 Performance and Mixed Time-Delays

2011 ◽  
pp. 1208-1232
Author(s):  
Hamid Reza Karimi
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Mixed Time Delays ◽  
Initial States ◽  
Delayed State Feedback ◽  
Delay Dependent

An exponential H8 synchronization method is addressed for a class of uncertain master and slave neural networks with mixed time-delays, where the mixed delays comprise different neutral, discrete and distributed time-delays. An appropriate discretized Lyapunov-Krasovskii functional and some free weighting matrices are utilized to establish some delay-dependent sufficient conditions for designing a delayed state-feedback control as a synchronization law in terms of linear matrix inequalities under less restrictive conditions. The controller guarantees the exponential H8 synchronization of the two coupled master and slave neural networks regardless of their initial states. Numerical simulations are provided to demonstrate the effectiveness of the established synchronization laws.

Robust multiobserver design for discrete uncertain nonlinear systems with time-varying delay

2016 ◽  
Vol 40 (1) ◽  
pp. 191-201 ◽  
Author(s):  
Samah Ben Atia ◽  
Anis Messaoud ◽  
Ridha Ben Abdennour
Keyword(s):  
Nonlinear Systems ◽  
Sufficient Conditions ◽  
Operating Regime ◽  
Linear Matrix ◽  
Time Varying ◽  
Uncertain Nonlinear Systems ◽  
Time Varying Delay ◽  
Partial Models ◽  
Delay Dependent ◽  
Varying Delay

In this paper, a robust multiobserver is proposed for the state estimation of discrete-time uncertain nonlinear systems with time-varying delay. The designed multiobserver is based on the decoupled multimodel approach. Unlike the classically used multimodel structures, the decoupled multimodel provides a flexibility of modelling. Indeed, the partial models’ structures can be adapted to the complexity of the system in each operating regime, thus the partial models can be with different dimensions. Delay-dependent sufficient conditions for the synthesis of a robust multiobserver against norm-bounded parametric uncertainties and in the presence of measurement noise are established in terms of linear matrix inequalities. A simulation example is given to illustrate the effectiveness of the designed multiobserver.

scholarly journals New Delay-Dependent Stability Criteria for Uncertain Neutral Systems with Mixed Time-Varying Delays and Nonlinear Perturbations

2009 ◽  
Vol 2009 ◽  
pp. 1-22 ◽  
Author(s):  
Hamid Reza Karimi ◽  
Mauricio Zapateiro ◽  
Ningsu Luo
Keyword(s):  
Sufficient Conditions ◽  
Distributed Delay ◽  
Linear Matrix ◽  
Time Varying ◽  
Neutral Systems ◽  
Neutral Delay ◽  
Change Of Variables ◽  
Parameter Perturbations ◽  
The Stability ◽  
Delay Dependent

The problem of stability analysis for a class of neutral systems with mixed time-varying neutral, discrete and distributed delays and nonlinear parameter perturbations is addressed. By introducing a novel Lyapunov-Krasovskii functional and combining the descriptor model transformation, the Leibniz-Newton formula, some free-weighting matrices, and a suitable change of variables, new sufficient conditions are established for the stability of the considered system, which are neutral-delay-dependent, discrete-delay-range-dependent, and distributed-delay-dependent. The conditions are presented in terms of linear matrix inequalities (LMIs) and can be efficiently solved using convex programming techniques. Two numerical examples are given to illustrate the efficiency of the proposed method.

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