LMIs in Control/Stability Analysis/Continuous Time/Transient State Bound for Non-Autonomous LTI Systems

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The System[edit | edit source]

For a continuous-time LTI system with a state-space representation of:

where , and x(0) = x0,

the transient bound can be evaluated with the following LMI.

The Data[edit | edit source]

, and x(0) = x0.

The LMI:[edit | edit source]

The Euclidean norm of the state satisfies:

if there exists and , where P > 0, such that:

if x0 = 0 and u is a unit-energy input (), then the above LMIs ensure that

Conclusion[edit | edit source]

By using this LMI the transient state bound can be analyzed for a given non-autonomous LTI system.

Implementation[edit | edit source]

The LMI given above can be implemented and solved using a tool such as YALMIP, along with an LMI solver such as MOSEK.

Related LMIs[edit | edit source]

External Links[edit | edit source]