Discrete-Time H2-Optimal Dynamic Output Feedback Control
A discrete time system operates on a discrete time signal input and produces a discrete time signal output. They are used in digital signal processing, such as digital filters for images or sound. The class of discrete time systems that are both linear and time invariant, known as discrete time LTI systems.
A Dynamic Output feedback controller is designed for a Discrete Time system, to minimize the H2 norm of the closed loop system with exogenous input and performance output .
Discrete-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.
Discrete-Time H2-Optimal Full-State Feedback Control
The LMI formulation
H2 norm <
The controller is recovered by
where,
and the matrixes and satisfies
Given and , the matrices and can be found using a matrix decomposition, such as a LU decomposition or a Cholesky decomposition.
If , ≠ 0, and ≠ 0, then it is often simplest to choose in order to satisfy the equality constraint
The Discrete-Time H2-Optimal Dynamic Output feedback controller is the system
A link to CodeOcean or other online implementation of the LMI
MATLAB Code
[1] - Continuous Time H2 Optimal Dynamic Output Feedback Control
A list of references documenting and validating the LMI.