LMIs in Control/Stability Analysis/Discrete Time/DiscreteTimeStrongStabilizability

The System 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 The matrices . The Optimization Problem The system G is strongly stabilizable if there exist , , and , where , such that Conclusion: 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 -example code Related LMIs https://en.wikibooks.org/wiki/LMIsinControl/StabilityAnalysis/ContinuousTime/StrongStabilizability - Continuous Time Strong Stabilizability External Links 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.