LMIs in Control/Click here to continue/LMIs in system and stability Theory/Continuous-time strong stabilizability
The System edit
Consider the continous-time LTI system, with state-space realization (A,B,C,0)
where , , , and it and it is assumed that (A, B) is stabilizable, (A, C) is detectable, and the transfer matrix has no poles on the imaginary axis.
The Data edit
The matrices .
The Optimization Problem edit
The system G is strongly stabilizable if there exist , , and , where , such that
Conclusion: edit
where and , is the solution to the Lyapunov equation given by
Moreover, a controller that strongly stabilizes G is given by the state-space realization
Implementation edit
- [1] Example Code
Related LMIs edit
- https://en.wikibooks.org/wiki/LMIs_in_Control/Stability_Analysis/Discrete_Time/DiscreteTimeStrongStabilizability - Discrete Time Strong Stabilizability
External Links edit
- 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.