Guaranteed level-γ ℋ ∞ control in uncertain linear systems via linear matrix inequalities

1996 ◽  
Vol 65 (6) ◽  
pp. 913-924
Author(s):  
POOGYEON PARK ◽  
THOMAS KAILATH
Keyword(s):  
Linear Systems ◽  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Uncertain Linear Systems

Mixed H2/H∞ Control for State-Delayed Linear Systems and a LMI Approach to the Solution of Coupled AREs

2003 ◽  
Vol 125 (2) ◽  
pp. 249-253 ◽  
Author(s):  
M. D. S. Aliyu
Keyword(s):  
Control Problem ◽  
Linear Systems ◽  
Linear Matrix Inequalities ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Riccati Equations ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Lmi Approach ◽  
Alternative Approach

In this paper, the state-feedback mixed H2/H∞ control problem for state-delayed linear systems is considered. Sufficient conditions for the solvability of this problem are given in terms of the solution to a pair of algebraic Riccati equations similar to the nondelayed case. However, these Riccati equations are more difficult to solve than those arising in the pure H2,H∞ problems, and an alternative approach is to solve a pair of linear matrix inequalities (LMIs).

scholarly journals Fault Detection of Markov Jumping Linear Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-27 ◽  
Author(s):  
Wei Li ◽  
Fan Jiang ◽  
Zhongqiu Wang ◽  
Gongbo Zhou ◽  
Zhencai Zhu
Keyword(s):  
Fault Detection ◽  
Linear Systems ◽  
Linear Matrix Inequalities ◽  
Discrete Time ◽  
Reference Model ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Residual Generator ◽  
Stochastic Properties ◽  
Residual Generation

In this paper, the fault detection (FD) problems of discrete-time Markov jumping linear systems (MJLSs) are studied. We first focus on the stationary MJLS. The proposed FD system consists of two steps: residual generation and residual evaluation. A new reference model strategy is applied to construct a residual generator, such that it is robust against disturbances and sensitive to system faults. The generated residual signals are then evaluated according to their stochastic properties, and a threshold is computed for detecting the occurrences of faults. The upper bound of the corresponding false alarm rate (FAR) is also given. For the nonstationary MJLS, similar results are also obtained. All the solutions are presented in the form of linear matrix inequalities (LMIs). Finally, a numerical example is used to illustrate the results.

scholarly journals State Estimators for Uncertain Linear Systems with Different Disturbance/Noise Using Quadratic Boundedness

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Longge Zhang ◽  
Xiangjie Liu ◽  
Xiaobing Kong
Keyword(s):  
Linear Systems ◽  
Estimation Error ◽  
Measurement Noise ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
State Estimators ◽  
Sufficient Stability ◽  
Necessary And Sufficient ◽  
Uncertain Linear Systems ◽  
Sufficient Stability Conditions

This paper designs state estimators for uncertain linear systems with polytopic description, different state disturbance, and measurement noise. Necessary and sufficient stability conditions are derived followed with the upper bounding sequences on the estimation error. All the conditions can be expressed in the form of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the approach.

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