Discrete-Time H2-Optimal Dynamic Output Feedback Control
A Dynamic Output feedback controller is designed for a Continuous Time system, to minimize the H2 norm of the closed loop system with exogenous input and performance output .
Continuous-Time LTI System with state space realization
The matrices: System
Controller
The following feasibility problem should be optimized:
is minimized while obeying the LMI constraints.
Solve for and that minimize subject to
The controller is recovered by
where,
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 , and , then it is often simplest to choose in order to satisfy the equality constraint
The Continuous-Time H2-Optimal Dynamic Output feedback controller is the system
The LMI given above can be implemented and solved using a tool such as YALMIP, along with an LMI solver such as MOSEK.
Discrete Time H2 Optimal Dynamic Output Feedback Control
Continuous Time H∞ Optimal Dynamic Output Feedback Control
A list of references documenting and validating the LMI.