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LMIs in Control/Stability Analysis/Discrete Time/Transient Output Bound for Discrete-Time Autonomous LTI Systems
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The System
Consider the discrete-time LTI system with state-space realization
,
The Data
and
The LMI
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
This can be implemented in any LMI solver such as YALMIP, using an algorithmic solver like Gurobi.
Conclusion
By using this LMI the transient state bound can be analyzed for a given autonomous LTI system.
Related Links
LMIs in Control/Stability Analysis/Discrete Time/Transient Bound for Discrete-Time Non-Autonomous LTI Systems
External Links
LMI Properties and Applications in Systems, Stability, and Control Theory