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.

State feedback stabilization of linear descriptor time-varying delay systems

2020 ◽  
Vol 42 (12) ◽  
pp. 2191-2197 ◽  
Author(s):  
Piyapong Niamsup ◽  
Vu N Phat
Keyword(s):  
State Feedback ◽  
Sufficient Conditions ◽  
Feedback Stabilization ◽  
Descriptor Systems ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Delay Function ◽  
Time Varying Delay ◽  
Varying Delay

In this paper, the augmented Lyapunov-Krasovskii function approach combining with singular value decomposition method is developed for stabilization of linear descriptor systems with time-varying delay. The delay function is non-differentiable, but continuous and bounded. By introducing a set of improved Lyapunov-Krasovskii functionals we propose delay-dependent sufficient conditions for admissibility of the system in terms of linear matrix inequalities. Then, based on the obtained stability results the problem of stabilization is solved via state feedback controllers, which guarantees that the descriptor closed-loop system is admissible. An numerical example with simulation is provided to show the effectiveness of the theoretical result.

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.

Generalized H2 Filtering for Discrete-Time Switched Systems with Multiple Time-Varying Delays

2012 ◽  
Vol 562-564 ◽  
pp. 1646-1649 ◽  
Author(s):  
Rong You Zhang ◽  
Ni Zhang
Keyword(s):  
Discrete Time ◽  
Switched Systems ◽  
Filter Design ◽  
Design Method ◽  
Sufficient Conditions ◽  
Design Procedure ◽  
Jensen Inequality ◽  
Linear Matrix ◽  
Multiple Time ◽  
Time Varying

The generalized H2 filtering problem is investigated for linear discrete-time switched systems with multiple time-varying delays. By constructing the piecewise Lyapunov-Krasovskii functionals, employing Jensen inequality and slack variables, the delay-dependent sufficient conditions are derived for the filter-error system to be stable with a H2 performance. Based on the established results, the filter design method is presented in terms of the linear matrix inequalities (LMI). The design procedure is brief and easy to compute. The optimal filter can be solved with LMI toolbox of MATLAB directly. Finally, the simulation results illustrate the effectiveness and feasibility 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.

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 Resilient Robust Finite-TimeL2-L∞Controller Design for Uncertain Neutral System with Mixed Time-Varying Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Xia Chen ◽  
Shuping He
Keyword(s):  
Finite Time ◽  
State Feedback ◽  
Controller Design ◽  
Linear Matrix ◽  
Neutral System ◽  
Time Varying ◽  
Constraint Condition ◽  
Closed Loop System ◽  
Delayed System ◽  
Delay Dependent

The delay-dependent resilient robust finite-timeL2-L∞control problem of uncertain neutral time-delayed system is studied. The disturbance input is assumed to be energy bounded and the time delays are time-varying. Based on the Lyapunov function approach and linear matrix inequalities (LMIs) techniques, a state feedback controller is designed to guarantee that the resulted closed-loop system is finite-time bounded for all uncertainties and to satisfy a givenL2-L∞constraint condition. Simulation results illustrate the validity of the proposed approach.

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.

MASTER-SLAVE SYNCHRONIZATION OF NONAUTONOMOUS CHAOTIC SYSTEMS AND ITS APPLICATION TO ROTATING PENDULUMS

2012 ◽  
Vol 22 (06) ◽  
pp. 1250147 ◽  
Author(s):  
KE DING ◽  
QING-LONG HAN
Keyword(s):  
Chaotic Systems ◽  
Design Method ◽  
Sufficient Conditions ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Phase Locked Loops ◽  
Linear Matrix ◽  
Delayed Feedback Controller ◽  
Delay Dependent ◽  
Time Delayed Feedback

Some mathematical models in engineering and physics, such as rotating pendulums, governors and phase locked loops in circuits, can be described as nonautonomous systems in which there exist chaotic attractors. This paper investigates master-slave synchronization for two nonautonomous chaotic systems by using time-delayed feedback control. Firstly, three delay-dependent synchronization criteria, which are formulated in the form of linear matrix inequalities (LMIs), are established for complete synchronization, lag synchronization and anticipating synchronization, respectively. Secondly, sufficient conditions on the existence of a time-delayed feedback controller are derived by employing these newly-obtained synchronization criteria. The controller gain can be obtained by solving a set of LMIs. Finally, the synchronization criteria and the design method are applied to master-slave synchronization for rotating pendulum systems.

scholarly journals RobustH∞Control for Linear Stochastic Partial Differential Systems with Time Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Xisheng Dai ◽  
Feiqi Deng ◽  
Jianxiang Zhang
Keyword(s):  
Time Delay ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Linear Matrix ◽  
Mean Square ◽  
Feedback Controllers ◽  
Partial Differential ◽  
Mean Square Exponential Stability ◽  
Linear Matrix Inequality Approach

This paper investigates the problems of robust stochastic mean square exponential stabilization and robustH∞for stochastic partial differential time delay systems. Sufficient conditions for the existence of state feedback controllers are proposed, which ensure mean square exponential stability of the resulting closed-loop system and reduce the effect of the disturbance input on the controlled output to a prescribed level ofH∞performance. A linear matrix inequality approach is employed to design the desired state feedback controllers. An illustrative example is provided to show the usefulness of the proposed technique.

A New Approach to Robust and Non-Fragile Control of Uncertain T-S Fuzzy Systems with Interval Time-Delay

2013 ◽  
Vol 662 ◽  
pp. 801-806
Author(s):  
Li Li
Keyword(s):  
Fuzzy System ◽  
Fuzzy Systems ◽  
State Feedback ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Feedback Controllers ◽  
New Approach ◽  
Time Varying Delay ◽  
Delay Dependent ◽  
Varying Delay

This paper describes the synthesis of robust and non-fragile state feedback controllers for T-S fuzzy system with time-varying delay in a range and parameter uncertainties. A new method is proposed by de¯ning new Lyapunov functionals and introducing some free-weighting matrices. Impr oved delay-dependent results are presented.

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