LMIs in Control/Controller Synthesis/Continuous Time/Robust H2 State Feedback Control

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Robust State Feedback Control[edit | edit source]

For the uncertain linear system given below, and a scalar . The goal is to design a state feedback control in the form of such that the closed-loop system is asymptotically stable and satisfies.


The System[edit | edit source]

Consider System with following state-space representation.


where , , , . For state feedback control

and are real valued matrix functions that represent the time varying parameter uncertainties and of the form


where matrices and are some known matrices of appropriate dimensions, while is a matrix which contains the uncertain parameters and satisfies.


For the perturbation, we obviously have

, for
, for


The Problem Formulation:[edit | edit source]

The state feedback control problem has a solution if and only if there exist a scalar , a matrix , two symmetric matrices and satisfying the following LMI's problem.

The LMI:[edit | edit source]



where is the definition that is need for the above LMI.


Conclusion:[edit | edit source]

In this case, an state feedback control law is given by .


External Links [edit | edit source]

  • LMIs in Control Systems Analysis, Design and Applications - Duan and Yu
  • A course on LMIs in Control by Matthew Peet.
  • LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.