LMIs in Control/pages/Discrete-Time H2 Norm

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Discrete-Time H2 Norm

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.

Discrete-Time LTI systems' H2 norm can be found by solving a LMI.

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 Bounded Real Lemma

The LMI formulation

H2 norm <

Conclusion:[edit | edit source]

The H2 norm is the minimum value of that satisfies the LMI condition.

Implementation[edit | edit source]

A link to CodeOcean or other online implementation of the LMI

Related LMIs[edit | edit source]

[1] - Continuous time H2 norm.

External Links[edit | edit source]

A list of references documenting and validating the LMI.

Return to Main Page:[edit | edit source]