Download Advanced Takagi‒Sugeno Fuzzy Systems: Delay and Saturation by Abdellah Benzaouia, Ahmed El Hajjaji PDF

By Abdellah Benzaouia, Ahmed El Hajjaji

This monograph places the reader in contact with a decade’s worthy of recent advancements within the box of fuzzy regulate in particular these of the preferred Takagi-Sugeno (T-S) style. New options for stabilizing keep an eye on research and layout according to a number of Lyapunov features and linear matrix inequalities (LMIs), are proposed. the entire effects are illustrated with numerical examples and figures and a wealthy bibliography is supplied for additional investigation.

Control saturations are taken into consideration in the fuzzy version. the idea that of confident invariance is used to acquire enough asymptotic balance stipulations for the bushy procedure with restricted regulate within a subset of the kingdom space.

The authors additionally ponder the non-negativity of the states. this can be of useful significance in lots of chemical, actual and organic procedures that contain amounts that experience intrinsically consistent and non-negative signal: focus of gear, point of beverages, and so on. effects for linear platforms are then prolonged to linear platforms with hold up. it's proven that LMI concepts can often deal with the recent constraint of non-negativity of the states while care is taken to take advantage of an sufficient Lyapunov functionality. From those foundations, the next extra difficulties also are handled:

· asymptotic stabilization of doubtful T-S fuzzy platforms with time-varying hold up, concentrating on delay-dependent stabilization synthesis in keeping with parallel dispensed controller (PDC);

· asymptotic stabilization of doubtful T-S fuzzy platforms with a number of delays, concentrating on delay-dependent stabilization synthesis in accordance with PDC with effects acquired less than linear programming;

· layout of delay-independent, observer-based, H-infinity keep watch over for T–S fuzzy platforms with time various hold up; and

· asymptotic stabilization of 2-D T–S fuzzy systems.

Advanced Takagi–Sugeno Fuzzy Systems offers researchers and graduate scholars drawn to fuzzy keep an eye on structures with extra techniques dependent LMI and LP.

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Additional info for Advanced Takagi‒Sugeno Fuzzy Systems: Delay and Saturation

Example text

Q rr for i, j = 1, 2, . . t. the pairs (i, j) such that h i (z(t))h j (z(t)) = 0, ∀t. 55) T G ij + G ji G ij + G ji P 2 2 ⎡ ⎤ Q 11 . . Q 1r ⎢ .. . ⎥ ⎣ . . 57) Q r 1 . . Q rr for i, j = 1, 2, . . t. the pairs (i, j) such that h i (z(t))h j (z(t)) = 0, ∀t. The determination of gains K j ( j = 1, 2, . . 8 into an equivalent problem in the form of linear matrix inequalities [22] that can be solved by convex optimization tools. 54). 58) + Sii < 0 Ai X + X Ai + A j X + X A j + Bi Y j + Y jT BiT + B j Yi + YiT B Tj + Sij + SijT < 0, i < j ⎤ S11 .

IF z 1 (t) is about a1 and z 2 (t) is about b2 , THEN, A(z 1 , z 2 ) = A(a1 , b2 ) = A2 . IF z 1 (t) is about b1 and z 2 (t) is about a2 , THEN, A(z 1 , z 2 ) = A(b1 , a2 ) = A3 . IF z 1 (t) is about b1 and z 2 (t) is about b2 , THEN, A(z 1 , z 2 ) = A(b1 , b2 ) = A4 . The membership functions are given by: h 1 (t) = f 11 (t) f 21 (t), h 2 (t) = f 11 (t) f 22 (t), h 3 (t) = f 12 (t) f 21 (t), h 4 (t) = f 12 (t) f 22 (t); z i (t) − bi f i1 (t) = , ai − bi f i2 (t) = 1 − f i1 (t) = ai − z i (t) , i = 1, 2.

Sr 1 . . 15 ⎤ S1r .. ⎥ > 0. 7, we consider the following example. 7. 7, respectively. In Fig. 2, the marks denote the LMI feasibility for the four theorems. It can be noted from Fig. 7 gives the most relaxed results. 2 Nonquadratic Lyapunov Functions To further reduce the conservatism introduced by the choice of a quadratic Lyapunov function, many studies have proposed methods using nonquadratic Lyapunov functions, such as piecewise quadratic Lyapunov functions proposed by Johanson et al.

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