LMIs in Control/Stability Analysis/Discrete Time/Transient Impulse Response Bound
The System
editConsider the single-input multi-output discrete-time LTI system with state-space realization
,
The Data
edit, , 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
edit
if there exist and where , such that
and
Implementation
editThis can be implemented in any LMI parser such as YALMIP which can implement a solver like Mosek to return a solution.
Conclusion
editBy using this LMI the transient state bound can be analyzed for a given autonomous LTI system.
Related Links
editReferences
editCaverly, Ryan; Forbes, James (2021). LMI Properties and Applications in Systems, Stability, and Control Theory.