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