LMIs in Control/Stability Analysis/Discrete Time/Transient Bound for Discrete-Time Non-Autonomous LTI Systems
The System
editFor 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, and
The LMI:
editThe 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
editBy using this LMI the transient state bound can be analyzed for a given non-autonomous LTI system.
Implementation
editThe LMI given above can be implemented and solved using a tool such as YALMIP, along with an LMI solver such as MOSEK.
Related LMIs
editExternal Links
edit- LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes.