I want to formulate this problem in LMI, so that i can solve using LMIEDIT toolbox of matlab.
Here A and B are system matrix, and deltaA is uncertainty in the A matrix, the value of deltaA is not known, but the maximum bound of deltaA(2-norm) is known i.e. gamma. And i have to design K such that closed loop system is stable. This is a statefeedback problem.
%%% Problem
(A+deltaA+B*K)T*X+X*(A+deltaA+B*K)
A new approach has been exposed recently for the synthesis of sets of controllers. Among other features, this approach handles the fragility problem. These promising results, developed for static-output feedback synthesis, suffer from being formulated as non convex optimisation problems. The aim of the article is to explore the distinctive case of state-feedback control. Convex LMI optimisation problems are derived for resilient (non-fragile) control with H/sub /spl infin// guaranteed performance. The essential contribution is that well-known LMI results for state-feedback design can be easily extended to the design of resilient control.
http://ieeexplore.ieee.org/document/1428662/
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