Uniform asymptotic stability of a class of interconnected systems with structural perturbations (Q2740287)

Here, a large scale system of the form [see \textit{Lj. T. Grujić}, \textit{A. A. Martynyuk} and \textit{M. Ribbens-Pavella}, Large scale systems stability under structural and singular perturbations. Lecture Notes in Control and Information Sciences, 92. Berlin etc.: Springer-Verlag (1987; Zbl 0649.93003)] NEWLINE\[NEWLINE\dot x_i=g_i(t,x_i)+S_i(t)h_i(t,x,p_i),\quad i=1,\ldots,s,NEWLINE\]NEWLINE is considered with \(x_i\in \mathbb R^{n_i}\), \(x=(x_1,\ldots,x_s)\), \(S_i=[s_{i1}I_i,\ldots,s_{iN}I_i]\), \(s_{ij}\in {0,1}\). The authors obtain a number of conditions under which the Lyapunov stability properties of the whole system is inferred from the properties of interconnected subsystems without using information about stability properties of disconnected subsystems. For this purpose matrix Lyapunov functions are used.NEWLINENEWLINENEWLINENote that the paper is not easy for reading because each theorem announced contains more than a dozen of conditions.NEWLINENEWLINENEWLINESee also the papers of \textit{A. A. Martynyuk} and \textit{I. P. Stavroulakis} [Ukr. Mat. Zh. 51, No. 6, 784-795 (1999; Zbl 0039.34045)], \textit{A. A. Martynyuk} and \textit{K. A. Begmuratov} [Ukr. Mat. Zh. 49, No. 4, 548-557 (1997; Zbl 0887.93062)].