H_∞ Control And The Analysis Of False Data Injection Attacks In Discrete Linear Time Invariant Systems

Many problems in the research field of system and control can be formalized into some optimization problems with constraints.Since the state space method was introduced into system and control research,many problems have been possible to be modeled as optimization problems with Linear Matrix Inequation(LMI)constraints.Facilitated by a bunch of efficient and user-friendly software that aims at solving LMI,LMI method shows great value in system and control research.This thesis starts with LMI method and search for its possible applications in nowadays system and control research.Based on discrete time invariant systems,it focuses on two topics:model-free H∞ control and Cyber Physical System(CPS)security.H∞ control problems are usually considered under the condition that the model parameters of the system are known.But in many real circumstances,the model parameters are hard to acquire.Hence,it’s necessary to consider model-free H∞ control techniques.In this thesis,an PI-based model-free H∞ control algorithm for discrete linear time invariant(LTI)systems is proposed.Particularly,a method to substitute state data by Input/Output(I/O)data is used to make the algorithm independent from state data which is usually hard to get,thus expands the application field of the algorithm.CPS heavily relies on wireless communication networks for information transmitting,which makes it vulnerable from malicious attacks.In this thesis,a False Data Injection Attack(FDIA)aiming at CPS is studied.First,the notions γ stealthiness and β strength are proposed.Then,the maximal β strength of the studied FDIA under the premise that it’s γstealthiness was calculated with LMI techniques.On the one hand,the notions of γstealthiness and β strength proposed can be used for the analysis of other classes of CPS attacks.On the other hand,the quantitative properties of the studied FDIA acquired can be used as references in CPS security design.