By El-Kébir Boukas
This publication bargains with the category of singular platforms with random abrupt alterations sometimes called singular Markovian bounce platforms. Many difficulties like stochastic balance, stochastic stabilization utilizing kingdom suggestions regulate and static output keep watch over, Hinfinity keep watch over, filtering, assured expense regulate and combined H2/Hinfinity keep watch over and their robustness are tackled. keep an eye on of singular structures with abrupt adjustments examines either the theoretical and sensible points of the keep an eye on difficulties taken care of within the quantity from the perspective of the structural houses of linear systems.
The conception provided within the assorted chapters of the quantity are utilized to examples to teach the usefulness of the theoretical effects. regulate of singular platforms with abrupt adjustments is a wonderful textbook for graduate scholars in strong regulate thought and as a reference for tutorial researchers up to speed or arithmetic with curiosity on top of things conception. The reader must have accomplished first-year graduate classes in likelihood, linear algebra, and linear structures. it's going to even be of significant worth to engineers practicing in fields the place the structures could be modeled by way of singular platforms with random abrupt changes.
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Additional info for Control of Singular Systems with Random Abrupt Changes
This problem, either for the deterministic framework or the stochastic one, has attracted many researchers from mathematical and control communities and many results on the subject have been reported in the literature. For more details on this topic, we refer the reader to [66, 102] for the deterministic framework and to [27, 14, 95, 65] for the stochastic framework and the references therein. For the class of systems we are considering in this book only few results have been reported in the literature.
3 Let εP = (εP (1), · · · , εP (N)) be a given set of positive scalars. 4 Let εP be a given positive scalar. 18) j=1, j i with the following constraints: εP P + P ≥ E (i)P = P E(i) ≥ 0 . 19) < 0. < 0 this condition gives: P A(i) + A (i)P < 0 . 20) we get the following results. 5 Let ε = (ε(1), · · · , ε(N)) be a given set of positive scalars. 21) j=1, j i with the following constraints: ε(i) P (i)P(i) ≥ E (i)P(i) = P (i)E(i) ≥ 0 . 4 We can transform the conditions of the previous corollary into an LMI setting.
8) The stabilizing controller gain is given by K(i) = Y(i)X −1 (i), K(i) ∈ Rm×n , i ∈ S . 1 The results we developed in the previous theorem can be extended easily to the mode-dependent εP ( j), ∀ j ∈ S case. If we consider that the parameter εP is mode-dependent, we get the following results. 1 Let εP = (εP (i), · · · , εP (N)) be a given set of positive scalars. 9) ⎢⎣ i ⎦ Si (X) 0 −Xi (X) where J0 (i) = A(i)X(i) + X (i)A (i) + B(i)Y(i) + Y (i)B (i) + λii X (i)E (i) , Xi (X) = diag −εP (1)I + X (1) + X(1), · · · , −εP (i − 1)I + X (i − 1) + X(i − 1), −εP (i + 1)I + X (i + 1) + X(i + 1), · · · , −εP (N)I + X (N) + X(N) , Si (X) = λi1 X (i), · · · , ··· , Zi (X) = λii−1 X (i), λiN X (i) , εP (1)λi1 X (i), · · · , ··· , λii+1 X (i), εP (i − 1)λii−1 X (i), εP (i + 1)λii+1 X (i), εP (N)λiN X (i) , with the following constraints: εP (i) X(i) + X (i) ≥ X (i)E (i) = E(i)X(i) ≥ 0 .
Control of Singular Systems with Random Abrupt Changes by El-Kébir Boukas