scholarly journals H∞Controller Design for Asynchronous Hybrid Systems with Multiple Delays

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
Xiaoqiang Sun ◽  
Weijie Mao
Keyword(s):  
Hybrid Systems ◽  
Controller Design ◽  
Linear Matrix ◽  
Multiple Delays ◽  
Data Systems ◽  
Sampled Data ◽  
State Augmentation ◽  
Delay Dependent ◽  
Symplectic Pair ◽  
Delay Dependent Stability

Solutions for theH∞synthesis problems of asynchronous hybrid systems with input-output delays are proposed. The continuous-time lifting approach of sampled-data systems is extended to a hybrid system with multiple delays, and some feasible formulas to calculate the operators of the equivalent discrete-time (DT) system are given. Different from the existing methods derived from symplectic pair theory or by state augmentation, a Lyapunov-Krasovskii functional to solve the synthesis problem is explicitly constructed. The delay-dependent stability conditions we obtained can be described in terms of nonstrict linear matrix inequalities (LMIs), which are much more convenient to be solved by LMI tools.

Delay-Dependent Stability of Cellular Neural Networks with Multiple Delays

2014 ◽  
Vol 598 ◽  
pp. 718-722 ◽  
Author(s):  
Grienggrai Rajchakit
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Bp Neural Network ◽  
Cellular Neural Networks ◽  
Stability And Convergence ◽  
Linear Matrix ◽  
Multiple Delays ◽  
Multiple Weights ◽  
Delay Dependent ◽  
Delay Dependent Stability

Back propagation (BP) neural network is used to approximate the dynamic character of nonlinear discrete-time system. Considering the unmodeling dynamics of the system, the weights of neural network are updated by using a dead-zone algorithm and a robust adaptive controller based on the BP neural network is proposed. For the situation that jumping change parameters exist, multiple neural networks with multiple weights are built to cover the uncertainty of parameters, and multiple controllers based on these models are set up. At every sample time, a performance index function based on the identification error will be used to choose the optimal model and the corresponding controller. Different kinds of combinations of fixed model and adaptive model will be used for robust multiple models adaptive control (MMAC). The proof of stability and convergence of MMAC are given, and the significant efficacy of the proposed methods is tested by simulation. This paper deals with the problem of delay-dependent stability criterion of delay-difference system with multiple delays of cellular neural networks. Based on quadratic Lyapunov functional approach and free-weighting matrix approach, some linear matrix inequality criteria are found to guarantee delay-dependent asymptotical stability of these systems. And one example illustrates the exactness of the proposed criteria.

IMPULSIVE EFFECTS ON STABILITY OF A CLASS OF NONLINEAR NEURAL NETWORKS WITH MULTIPLE DELAYS

2009 ◽  
Vol 19 (09) ◽  
pp. 3143-3148
Author(s):  
QINGHUA ZHOU ◽  
LI WAN ◽  
QUNJIAO ZHANG
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Linear Matrix ◽  
Multiple Delays ◽  
Lyapunov Functionals ◽  
Matrix Inequality ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Stability Results ◽  
Nonlinear Neural Networks

The global asymptotic stability (GAS) for a class of nonlinear impulsive neural networks with multiple delays are discussed. By skillfully constructing suitable Lyapunov functionals and the linear matrix inequality (LMI) technique, a new sufficient delay-dependent stability criterion is derived. The proposed stability results are less conservative than some recently known ones in the literature, which is demonstrated via two examples with simulation.

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 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.

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.

Standardizability and H2-Optimization of Sampled-Data Systems with Multiple Delays

2019 ◽  
Vol 80 (3) ◽  
pp. 413-428 ◽  
Author(s):  
E. N. Rosenwasser ◽  
B. P. Lampe ◽  
W. Drewelow ◽  
T. Jeinsch
Keyword(s):  
Multiple Delays ◽  
Data Systems ◽  
Sampled Data ◽  
H2 Optimization

scholarly journals A New Stability Criterion for Systems with Distributed Time-Varying Delays via Mixed Inequalities Method

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Jun-kang Tian ◽  
Yan-min Liu
Keyword(s):  
Linear Matrix Inequalities ◽  
Stability Criterion ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Numerical Examples ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
New Inequalities

This paper is concerned with the delay-dependent stability of systems with distributed time-varying delays. The novelty relies on the use of some new inequalities which are less conservative than some existing inequalities. A less conservative stability criterion is obtained by constructing some new augmented Lyapunov–Krasovskii functionals, which are given in terms of linear matrix inequalities. The effectiveness of the presented criterion is demonstrated by two numerical examples.

New Delay-Dependent Robust Stability Criterion for Uncertain Stochastic Systems with Time-Varying Delays

2012 ◽  
Vol 461 ◽  
pp. 633-636
Author(s):  
Cheng Wang
Keyword(s):  
Robust Stability ◽  
Stability Criterion ◽  
Stochastic Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Weighting Matrix ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

The problem of delay-dependent robust stability of uncertain stochastic systems with time-varying delay is discussed in this paper. Based on the Lyapunov-Krasovskii theory and free-weighting matrix technique, new delay-dependent stability criterion is presented. The criterion is in terms of linear matrix inequality (LMI) which can be solved by various available algorithms.

An Improved Delay-Dependent Stability Criterion for a Class of Lur’e Systems of Neutral Type

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
K. Ramakrishnan ◽  
G. Ray
Keyword(s):  
Stability Analysis ◽  
Stability Criterion ◽  
Time Derivative ◽  
Neutral Type ◽  
Linear Matrix ◽  
Lur’E Systems ◽  
The Stability ◽  
Delay Dependent ◽  
Bounded Nonlinearity ◽  
Delay Dependent Stability

In this paper, we consider the problem of delay-dependent stability of a class of Lur’e systems of neutral type with time-varying delays and sector-bounded nonlinearity using Lyapunov–Krasovskii (LK) functional approach. By using a candidate LK functional in the stability analysis, a less conservative absolute stability criterion is derived in terms of linear matrix inequalities (LMIs). In addition to the LK functional, conservatism in the proposed stability analysis is further reduced by imposing tighter bounding on the time-derivative of the functional without neglecting any useful terms using minimal number of slack matrix variables. The proposed analysis, subsequently, yields a stability criterion in convex LMI framework, and is solved nonconservatively at boundary conditions using standard LMI solvers. The effectiveness of the proposed criterion is demonstrated through a standard numerical example and Chua’s circuit.

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