LMIs in Control/Stability Analysis/Discrete Time/Transient Output Bound for Discrete-Time Autonomous LTI Systems
The System edit
Consider the discrete-time LTI system with state-space realization
,
The Data edit
and
The LMI edit
The Euclidean norm of the output satisfies
if there exist \bold P \in\mathbb S^n and \gamma \in\mathbb R_{>0}, where \bold P > 0, such that
,
Implementation edit
This can be implemented in any LMI solver such as YALMIP, using an algorithmic solver like Gurobi.
Conclusion edit
By using this LMI the transient state bound can be analyzed for a given autonomous LTI system.