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LMIs in Control/Stability Analysis/Discrete Time/Transient Impulse Response Bound
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The System
Consider the single-input multi-output discrete-time LTI system with state-space realization
,
The Data
, , and , and it is assumed that is invertible. Let . be the unit impulse response of the system. The Euclidian Norm of the impulse response satisfies the following LMI.
The LMI
if there exist and where , such that
and
Implementation
This can be implemented in any LMI parser such as YALMIP which can implement a solver like Mosek to return a solution.
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
References
LMI Properties and Applications in Systems, Stability, and Control Theory Caverly Ryan 2021 Forbes James