Large-Scale Dynamic Systems: Stability and Structure by Dragoslav D. Siljak

By Dragoslav D. Siljak

This special interdisciplinary strategy examines the difficult relationships one of the balance and buildings of huge dynamic structures. Its definitions of enormous structures when it comes to their interconnected subsystems supply a computationally appealing strategy, with functions starting from those involving spacecraft and tool structures to elements of ecology and economics. 1978 version.

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Example text

9) represents the basic structu ental fundam the called the system; in the following developments, it is the enting repres E E2. 3 interconnection matrix. , ental fundam the from ed structural perturbations of the system are obtain We may interconnection matrix E by replacing unit elements with zeros. 7). Consid and b2 are not zero. 5) represent is used to model two interacting species, ~ and b2 may either des pestici of uences conseq the reflect or t, availability of food in the habita applied to the community.

Therefore, as shown in the following section, the chosen decomposition will allow us to study explicitly the effect on overall system stability of varying the velocity w. It is obvious, however, that there is no connective stability in the true sense of the term, since the two subsystems cannot be physically disconnected from each other (although the two motions corresponding to the two deflections become decoupled as the angular velocity decreases to zero). To illustrate the connectivity aspect of decompositions, let us consider a two-predator, two-prey community described by the equations h1 = a1h1- auht- '/IhiPI- a12h2, jJ..

85) ents ~ 2 (t), ~1{t) of the and replacing its unit elements with the elem matrix E. We also recall that x == (x1, x2)T. 71) x2 == A2x2. lity of ~. we require Since we wan t to establish the connective stabi 0 the system ~ can be that ~ and ~1 be stable. 71), and instability of eithe instability of ~. , G1 there matr ite that for any choice of the positive defin of the Liapunov ions solut as exist positive definite matrices lit, H2 matrix equations AT H,. + HiA. g. l3 ). 87). l(H;), i = 1, 2.

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