LMIs in Control/pages/dt mixed H2 Hinf optimal output feedback control

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WIP, Description in progress

This part shows how to design dynamic outpur feedback control in mixed and sense for the continuous time.

Problem[edit | edit source]

Consider the discrete-time generalized LTI plant with minimal state-space realization

Theorem[edit | edit source]

A continuous-time dynamic output feedback LTI controllerwith state-space realization is to be designed to minimize the norm of the closed-loop transfer matrix from the exogenous input to the performance output while ensuring the H∞ norm of the closed-loop transfer matrix from the exogenous input to the performance output is less than , where

,

,

,

,

,

,

and .


Synthesis Method[edit | edit source]

Solve for and that minimizes subjects to

,

,

,

tr

where .

The controller is recovered by

, and the matrices and satisfy . If , then and .

Given and , the matrices and can be found using a matrix decomposition, such as a LU decomposition or a Cholesky decomposition.

If then it is often simplest to choose in order to satisfy the equality constraint .



WIP, additional references to be added

External Links[edit | edit source]

A list of references documenting and validating the LMI.

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