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T. J¨onsson for some ε > 0. 1 (c) it follows that (I − H ∆0 )−1 ∈ An×n and hence that ψ (s, 0, 0) has no zeros in the closed right half-plane. By continuity ψ (s, θ , α ) satisfies ψ ( jω , θ , α ) > 0, ∀ω ∈ R ∪ {∞}, θ ∈ [0, 1] for small enough α > 0. g. 18 in [1]. Once again, by continuity it follows that ψ (s, 1, 0) also has no zeros in closed right half plane and hence (I − H ∆ )−1 ∈ An×n and the claim is proven. 22) we use the following version of Finsler’s lemma. 2. Let B ∈ Cn×m , m < n and B⊥ ∈ C(n−m)×n be such that (1) B⊥ B = 0, (2) rank B B∗⊥ = n, and (3) B⊥ B∗⊥ I.
Atlanta, GA (2010) 11. : Convex Analysis. Princeton University Press, Princeton, NJ (1970) 12. : Passivity gains and the “secant condition” for stability. Systems Control Letters 55(3), 177–183 (2006) 13. : Input-Output Analysis of Large Scale Interconnecred Systems. Lecture Notes in Control and Information Sciences. Springer-Verlag, Berlin (1981) 14. : Robust congestion control for the Internet (2002). Unpublished Chapter 2 Optimal Controller Synthesis for a Decentralized Two-Player Linear-Quadratic Regulator via Spectral Factorization John Swigart and Sanjay Lall Abstract We develop controller synthesis algorithms for decentralized control problems.
It provides a compact way of modeling very general networks as is illustrated in Fig. 1. An effective approach to large scale systems analysis is to first characterize the subsystem dynamics and then to verify that the interconnection operator satisfies the complementary aggregate criterion. In this chapter, we propose an alternative approach, where we first find a characterization of the interconnection operator and then verify that the subsystem dynamics satisfy the complementary criterion. This approach is sometimes useful when a large number of structurally similar systems are interconnected over a network with some inherent structure.