LMIs in Control/pages/Discrete-Time Lyapunov Stability

Discrete-Time Lyapunov Stability


The System

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Discrete-Time System

 

The Data

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The matrices  .

The Optimization Problem

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The following feasibility problem should be solved:

Find P obeying the LMI constraints.

The LMI:

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Discrete-Time Lyapunov Stability

The LMI formulation

 

Conclusion:

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If there exists a   satisfying the LMI then,   and the equilibrium point   of the system is Lyapunov stable.

Implementation

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  • [] - MATLAB implementation of the LMI.
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Continuous_Time_Lyapunov_Inequality - Lyapunov_Inequality

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A list of references documenting and validating the LMI.


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