LMIs in Control/Stability Analysis/Discrete Time/Transient Bound for Discrete-Time Non-Autonomous LTI Systems
Jump to navigation
Jump to search
The System[edit | edit source]
For a discrete-time LTI system with a state-space representation of:
where , and ,
the transient bound can be analyzed with the LMI below.
The Data[edit | edit source]
, and
The LMI:[edit | edit source]
The Euclidean norm of the state satisfies:
if there exists some 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.