LMIs in Control/Click here to continue/LMIs in system and stability Theory/Discrete-time strong stabilizability
Appearance
The System
[edit | edit source]Consider the continous-time LTI system, with state-space realization ()
where , , , and it and it is assumed that (),is stabilizable, () is detectable, and the transfer matrix has no poles on the imaginary axis.
The Data
[edit | edit source]The matrices .
The Optimization Problem
[edit | edit source]The system G is strongly stabilizable if there exist , , and , where , such that
Conclusion:
[edit | edit source]where and , is the solution to the discrete-time Lyapunov equation given by
Moreover, a controller that strongly stabilizes G is given by the state-space realization
Implementation
[edit | edit source]- [1]-example code
Related LMIs
[edit | edit source]- https://en.wikibooks.org/wiki/LMIsinControl/StabilityAnalysis/ContinuousTime/StrongStabilizability - Continuous Time Strong Stabilizability
External Links
[edit | edit source]- http://control.asu.edu/MAE598_frame.htm LMI Methods in Optimal and Robust Control- A course on LMIs in Control by Matthew Peet.\\
- https://https://arxiv.org/abs/1903.08599/ LMI Properties and Applications in Systems, Stability, and Control Theory] - A List of LMIs by Ryan Caverly and James Forbes.\\
- https://web.stanford.edu/~boyd/lmibook/ LMIs in Systems and Control Theory- A downloadable book on LMIs by Stephen Boyd.