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RECENT ADVANCES IN ROBUST CONTROL – NOVEL APPROACHES AND DESIGN METHODSE Part 3

Tham khảo tài liệu 'recent advances in robust control – novel approaches and design methodse part 3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Observer-Based Robust Control of Uncertain Fuzzy Models with Pole Placement Constraints 49 Remark 4 . Any kind of LMI region disk vertical strip conic sector may be easily used for Ds and DT. From lemma 2 and lemma 3 we have imposed the dynamics of the state as well as the dynamics of the estimation error. But from 10 the estimation error dynamics depend on the state. If the state dynamics are slow we will have a slow convergence of the estimation error to the equilibrium point zero in spite of its own fast dynamics. So in this paper we add an algorithm using the HX approach to ensure that the estimation error converges faster to the equilibrium point zero. We know from 10 that r. . e t 22hi z t hj z t Ai GCj -ABịKị e t i 1j 1 r r 43 22hi z t hj z t Sj AAi BJ x t i 1j 1 This equation is equivalent to the following system e e r r 22 hi z t hj z t i 1j 1 Ai GiCj KK A. - B K - re I 0 x 44 The objective is to minimize the L2 gain from x t to e t in order to guarantee that the error between the state and its estimation converges faster to zero. Thus we define the following HX performance criterion under zero initial conditions X J e1 t e t - Y1xt t x t dt 0 45 0 where Y e ĩ has to be minimized. Note that the signal x t is square integrable because of lemma 1. We give the following lemma to satisfy the H. performance. Lemma 4 If there exist symmetric positive definite matrix P2 matrices Wi and positive scalars Y 0 Pj 0 such as ra 0 i 1 . r rij r ji 0 i j r 46 With rij Z HbiP2 HtP2 -PjEUKị P2 Hbi -flijI 0 0 P2 Ha 0 -PijI 0 PijEbK 0 0 Uij 50 Recent Advances in Robust Control - Novel Approaches and Design Methods Zij - P2 A a p2 WiCj C W 1 jEEK ư _-1 2 T I Tjt TJ V I n Tjt TJ ij - Y 1 PjKjEbiEbiKj PijEaiEai Then the dynamic system r el A. XXhi z t hj z t _ e_l i-1 j-1 A GiCj K.K. 1 AAi ABK L LI r e 0 _ T x 47 satisfies the Hw performance with a L2 gain equal or less than Y 44 . Proof Applying the bounded real lemma Boyd al 1994 the system described by the following dynamics