New results on discrete-time bounded real lemma for singular systems: strict matrix inequality conditions

2003 ◽  
Author(s):  
Gaomin Zhang ◽  
Yingmin Jia
Keyword(s):  
Discrete Time ◽  
Singular Systems ◽  
Matrix Inequality ◽  
Bounded Real Lemma

A Bounded Real Lemma for Discrete-Time Markovian Jump Singular Systems

2013 ◽  
Vol 16 (1) ◽  
pp. 303-307 ◽  
Author(s):  
Jumei Wei ◽  
Rui Ma ◽  
Xiaowu Mu
Keyword(s):  
Discrete Time ◽  
Singular Systems ◽  
Markovian Jump ◽  
Bounded Real Lemma

New bounded real lemma for discrete-time singular systems

Automatica ◽  
2008 ◽  
Vol 44 (3) ◽  
pp. 886-890 ◽  
Author(s):  
Gaomin Zhang ◽  
Yuanqing Xia ◽  
Peng Shi
Keyword(s):  
Discrete Time ◽  
Singular Systems ◽  
Bounded Real Lemma

Input-Output Analysis of Environmental Protection Industry

2014 ◽  
Vol 1073-1076 ◽  
pp. 2700-2703
Author(s):  
Lei Jiang ◽  
Shou Zhong Hu ◽  
Xiao Xiao Xu
Keyword(s):  
Environmental Protection ◽  
Singular Systems ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Input Output ◽  
Output Analysis ◽  
Input Output Analysis ◽  
Sufficient Stability Condition ◽  
Sufficient Stability ◽  
Output System

This paper investigates the run of environmental protection industry input-output model. A new mathematic method is applied to study this kind of singular input-output system. With this new method, we need not convert singular systems into general linear systems. A sufficient stability condition under which an environmental protection industry input-output model is stable is proved. This condition is in the form of linear matrix inequality and can be easily tested by computers.

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 Fuzzy Stabilization for Nonlinear Discrete Ship Steering Stochastic Systems Subject to State Variance and Passivity Constraints

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Wen-Jer Chang ◽  
Bo-Jyun Huang ◽  
Po-Hsun Chen
Keyword(s):  
Linear Matrix Inequality ◽  
Discrete Time ◽  
Stochastic Systems ◽  
Fuzzy Controller ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Control Technique ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Ship Steering

For nonlinear discrete-time stochastic systems, a fuzzy controller design methodology is developed in this paper subject to state variance constraint and passivity constraint. According to fuzzy model based control technique, the nonlinear discrete-time stochastic systems considered in this paper are represented by the discrete-time Takagi-Sugeno fuzzy models with multiplicative noise. Employing Lyapunov stability theory, upper bound covariance control theory, and passivity theory, some sufficient conditions are derived to find parallel distributed compensation based fuzzy controllers. In order to solve these sufficient conditions, an iterative linear matrix inequality algorithm is applied based on the linear matrix inequality technique. Finally, the fuzzy stabilization problem for nonlinear discrete ship steering stochastic systems is investigated in the numerical example to illustrate the feasibility and validity of proposed fuzzy controller design method.

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