LMIs in Control/Click here to continue/Observer synthesis/Full-order state Observer

Full-Order State Observer The problem of constructing a simple full-order state observer directly follows from the result of Hurwitz detectability LMI's, Which essentially is the dual of Hurwitz stabilizability. If a feasible solution to the first LMI for Hurwitz detectability exist then using the results we can back out a full state observer such that is Hurwitz stable. The System where , , , at any . The Data The matrices are system matrices of appropriate dimensions and are known. The Optimization Problem The full-order state observer problem essential is finding a positive definite such that the following LMI conclusions hold. The LMI: 1) The full-order state observer problem has a solution if and only if there exist a symmetric positive definite Matrix and a matrix that satisfy Then the observer can be obtained as 2) The full-state state observer can be found if and only if there is a symmetric positive definite Matrix that satisfies the below Matrix inequality In this case the observer can be reconstructed as . It can be seen that the second relation can be directly obtained by substituting in the first condition. Conclusion: Hence, both the above LMI's result in a full-order observer such that is Hurwitz stable. External Links A list of references documenting and validating the LMI. LMIs in Control Systems Analysis, Design and Applications - Duan and Yu 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. LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd. Return to Main Page: