Sybase Architecture and Administration by John Kirkwood

By John Kirkwood

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F ≤ 0) stands for Zs. : Stability and Observer Design Using TS Models, STUDFUZZ 262, pp. 25–48. com © Springer-Verlag Berlin Heidelberg 2010 26 3 Stability Analysis of TS Fuzzy Systems semi-positive (resp. , the eigenvalues can be positive (resp. negative) or zero. , F = F T > 0, even if the explicit notation is omitted. With A, B ∈ Rn×n being two symmetric matrices A > B is equivalent to A − B > 0. A star (∗) in a matrix indicates a transposed quantity in the symmetric position. P (∗) P AT For instance, < 0 is equivalent to < 0.

Chapter 4 Observers for TS Fuzzy Systems In practical situations, not all state variables of a given system can be measured. In such cases, an observer has to be designed to estimate the unmeasured states based on the system model and the available input-output data. This chapter introduces the concept of observers used for TS fuzzy systems and reviews methods for designing observers such that the estimation error asymptotically converges to zero. We also briefly describe observer-based stabilization.

Q1m ⎜ Q21 Q22 . . Q2m ⎟ ⎟ ⎜ ⎜ .. ⎟>0 .. ⎝ . .. 6) Qm1 Qm2 . . Qmm for i = 1, 2, . . , m, j = i + 1, i + 2, . . , m. 2 are only sufficient. Nevertheless, some relaxations exist that also become necessary when the number of terms in the summations tends to infinity; Sala and Ari˜no (2007) proposed conditions that are based on Polya’s theorems, whereas Kruszewski et al. (2009) proposed conditions that are based on triangulation. Other works use more properties of the nonlinear functions wi (z), i = 1, 2, .

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