scholarly journals Method of Reduction of Variables for Bilinear Matrix Inequality Problems in System and Control Designs

2017 ◽  
Vol 47 (7) ◽  
pp. 1241-1256 ◽  
Author(s):  
Wei-Yu Chiu
Keyword(s):  
Matrix Inequality ◽  
Bilinear Matrix Inequality ◽  
And Control ◽  
Control Designs

scholarly journals A Nonlinear Systems Framework for Cyberattack Prevention for Chemical Process Control Systems †

Mathematics ◽  
2018 ◽  
Vol 6 (9) ◽  
pp. 169 ◽  
Author(s):  
Helen Durand
Keyword(s):  
Nonlinear Systems ◽  
Control Systems ◽  
Chemical Process ◽  
Property A ◽  
Control Laws ◽  
Industrial Control Systems ◽  
Plant Safety ◽  
And Control ◽  
Systems Framework ◽  
Control Designs

Recent cyberattacks against industrial control systems highlight the criticality of preventing future attacks from disrupting plants economically or, more critically, from impacting plant safety. This work develops a nonlinear systems framework for understanding cyberattack-resilience of process and control designs and indicates through an analysis of three control designs how control laws can be inspected for this property. A chemical process example illustrates that control approaches intended for cyberattack prevention which seem intuitive are not cyberattack-resilient unless they meet the requirements of a nonlinear systems description of this property.

scholarly journals Analysis of Robust Stability for a Class of Stochastic Systems via Output Feedback: The LMI Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Xin-rong Cong ◽  
Long-suo Li
Keyword(s):  
Linear Matrix Inequality ◽  
Robust Stability ◽  
Output Feedback ◽  
Stochastic Systems ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Convex Optimization Problem ◽  
Control Laws ◽  
The Stability ◽  
And Control

This paper investigates the robust stability for a class of stochastic systems with both state and control inputs. The problem of the robust stability is solved via static output feedback, and we convert the problem to a constrained convex optimization problem involving linear matrix inequality (LMI). We show how the proposed linear matrix inequality framework can be used to select a quadratic Lyapunov function. The control laws can be produced by assuming the stability of the systems. We verify that all controllers can robustly stabilize the corresponding system. Further, the numerical simulation results verify the theoretical analysis results.

The Application of Linear Algebra Algorithm in the Production of Linear Matrix Inequalities

2012 ◽  
Vol 192 ◽  
pp. 406-411
Author(s):  
Hui Zhang
Keyword(s):  
Problem Solving ◽  
Linear Algebra ◽  
Linear Matrix Inequalities ◽  
Polynomial Matrix ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Matrix Inequalities ◽  
Application System ◽  
And Control ◽  
Problem Data

Discusses the theory and symbolic of the algorithm gives another potential application, but also in the system and control. For example, for the question, has made with special structure, but LMI problem data, may cause factorizations LMI more compact. One can even imagine using the algorithm around, looking for the opportunity to LMI automatic eliminate variables, so simplify problem solving, before they get a lot of influence and a potential solutions. We describe theory, the algorithm can be used to factor in the non commuting variable polynomial matrix and application system switches and control problem into a linear matrix inequality.

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