By El-Kébir Boukas
This ebook bargains with the category of singular structures with random abrupt adjustments often referred to as singular Markovian leap structures. Many difficulties like stochastic balance, stochastic stabilization utilizing kingdom suggestions regulate and static output keep an eye on, Hinfinity regulate, filtering, assured price regulate and combined H2/Hinfinity regulate and their robustness are tackled. regulate of singular structures with abrupt adjustments examines either the theoretical and sensible facets of the keep watch over difficulties taken care of within the quantity from the perspective of the structural houses of linear systems.
The idea provided within the various chapters of the amount are utilized to examples to teach the usefulness of the theoretical effects. keep watch over of singular structures with abrupt alterations is a superb textbook for graduate scholars in powerful keep watch over thought and as a reference for tutorial researchers up to the mark or arithmetic with curiosity up to speed concept. The reader must have accomplished first-year graduate classes in chance, linear algebra, and linear platforms. it is going to even be of serious price to engineers practicing in fields the place the platforms might be modeled via singular platforms with random abrupt changes.
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Extra info for Control of Singular Systems with Random Abrupt Changes
5 Fig. 1. 0 ⎥⎥⎥⎥ . 0 ⎥⎥⎥⎥ . 2 The switching between the three modes is supposed to be described by the following transition rates: ⎡ ⎤ ⎢⎢⎢ −1 1 0 ⎥⎥⎥ ⎢⎢⎢ ⎥ Λ = ⎢⎢ 0 −2 2 ⎥⎥⎥⎥ . 0 ⎥⎥⎦ . 1098 The three matrices are nonsingular matrices, which implies that conditions of the first theorem are satisfied. 7, the system under study is piecewise regular, impulse-free and stochastically stable. A simulation of this system using MATLAB gives the behavior of the diﬀerent states in function of time t as illustrated in Fig.
Let us establish another way of stabilizing the class of systems we are considering. 5 the closedloop state equation when Acl (i) is replaced by its expression will be piecewise regular, impulse-free and stochastically stable if there exists a set of nonsingular matrices P = (P(1), · · · , P(N)), with P(i) ∈ Rn×n such that the following conditions hold for each i ∈ S: ⎧ ⎪ ⎪ εP P(i) + P (i) ≥ E (i)P(i) = P (i)E(i) ≥ 0 , ⎪ ⎪ ⎪ ⎨ A (i)P(i) + P (i)A(i) + K (i)B (i)P(i) + P (i)B(i)K(i) ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ +λii E (i)P(i) + Nj=1, j i εP λi j P( j) + P ( j) < 0 .
This chapter deals with the stabilization problem of the singular class of systems with random abrupt changes. The stochastic stabilizability and the robust stochastic stabilizability problems will be considered and LMI conditions will be developed. A state feedback controller that assures that the closed-loop state equation either for the nominal system or the uncertain one is piecewise regular, impulse-free and stochastically stable is designed in the LMI setting. The conditions we will develop in this chapter are tractable using commercial optimization tools like MATLAB LMI toolbox, YALMIP and SeDuMi (based on MATLAB) or Scilab.