LMIs in Control/Click here to continue/LMIs in system and stability Theory/Continuous-time Static Output Feedback Stabilizability

In view of applications, static feedback of the full state is not feasible in general: only a few of the state variables (or a linear combination of them, , called the output) can be actually measured and re-injected into the system. So, we are led to the notion of static output feedback The System Consider the continuous-time LTI system, with generalized state-space realization The Data The Optimization Problem This system is static output feedback stabilizable (SOFS) if there exists a matrix F such that the closed-loop system (obtained by replacing which means applying static output feedback) is asymptotically stable at the origin The LMI: LMI for Continuous Time - Static Output Feedback Stabilizability The system is static output feedback stabilizable if and only if it satisfies any of the following conditions: There exists a and , where , such that There exists a and , where , such that There exists a and , where , such that There exists a and , where , such that Conclusion On implementation and optimization of the above LMI using YALMIP and MOSEK (or) SeDuMi we get 2 output matrices one of which is the Symmeteric matrix (or ) and Implementation A link to the Matlab code for a simple implementation of this problem in the Github repository: https://github.com/yashgvd/LMI_wikibooks Related LMIs Discrete time Static Output Feedback Stabilizability Static Feedback Stabilizability External Links - LMI in Control Systems Analysis, Design and Applications LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet. LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes. D. d. S. Madeira and J. Adamy, "Static output feedback: An LMI condition for stabilizability based on passivity indices," 2016 IEEE Conference on Control Applications (CCA), Buenos Aires, 2016, pp. 960-965. Return to Main Page: