LMIs in Control/pages/Discrete Time H2 Optimal Full State Feedback Control
Discrete-Time H2-Optimal Full-State 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 full state feedback controller design for a Discrete Time system, to minimize the H2 norm of the closed loop system with exogenous input and performance output .
The System
[edit | edit source]Discrete-Time LTI System with state space realization
The Data
[edit | edit source]The matrices: System .
The Optimization Problem
[edit | edit source]The following feasibility problem should be optimized:
is minimized while obeying the LMI constraints.
The LMI:
[edit | edit source]Discrete-Time H2-Optimal Full-State Feedback Control
The LMI formulation
H2 norm <
Conclusion:
[edit | edit source]The H2-optimal full-state feedback gain is recovered by
Implementation
[edit | edit source]A link to CodeOcean or other online implementation of the LMI
MATLAB Code
Related LMIs
[edit | edit source][1] - Continuous Time H2 Optimal Full State Feedback Control
External Links
[edit | edit source]A list of references documenting and validating the LMI.
- LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
- LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes.
- LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.