LMIs in Control/Stability Analysis/Continuous Time/Transient State Bound for Non-Autonomous LTI Systems
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]
- LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes.