LMIs in Control/Observer Synthesis/Continuous Time/Reduced-Order State Observer

Reduced Order State Observer The Reduced Order State Observer design paradigm follows naturally from the design of Full Order State Observer. The System where , , , at any . The Data The matrices are system matrices of appropriate dimensions and are known. The Problem Formulation Given a State-space representation of a system given as above. First an arbitrary matrix is chosen such that the vertical augmented matrix given as is nonsingular, then Furthermore, let then the matrix pair is detectable if and only if is detectable, then let then a new system of the form given below can be obtained once an estimate of is obtained the full state estimate can be given as the reduced order observer can be obtained in the form. Such that for arbitrary control and arbitrary initial system values, There holds The value for can be obtain by solving the following LMI. The LMI: The reduced-order observer exists if and only if one of the two conditions holds. 1) There exist a symmetric positive definite Matrix and a matrix that satisfy Then 2) There exist a symmetric positive definite Matrix that satisfies the below Matrix inequality Then . By using this value of we can reconstruct the observer state matrices as Conclusion: Hence, we are able to form a reduced-order observer using which we can back of full state information as per the equation given at the end of the problem formulation given above. 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: