Lyapunov functions for a class of large-scale systems

Author

Sinha, A.S.C.

Author_Institution

Indiana University-Purdue University, Indianpolis, IN, USA

Volume

25

Issue

3

fYear

1980

fDate

6/1/1980 12:00:00 AM

Firstpage

558

Lastpage

560

Abstract

The behavior of solutions of a class of large-scale systems with the bounded coefficients of the form [1] has been studied. The function $V_{i}(x_{i},t)=A_{i}(t)x_{i}^{2}$ , whose coefficient $A_{i}(t)$ is bounded for all $t \\geq 0$ , gives the conditions on the Lyapunov function such that the system (1) is either asymptotically stable or unstable. Since the function of the form $e^{-t}x^{2}$ is not positive definite in the Lyapunov sense, a Lyapunov function of the form $V_{i}(x_{i},t)=e^{-Q_{i}(t)}x_{i}^{2}$ where $Q_{i}(t)$ is bounded is constructed which is positive definite in the Lyapunov sense. A systematic procedure for the construction of such a function is given. The approach is quite general. The method is inspired from the papers of Grujic and Siljak [1], Siljak [2], [3], Weissenberger [4], Bailey [5], and Michel et al. [7], [8].

Keywords

Asymptotic stability; Interconnected systems; Lyapunov functions; Nonlinear systems, continuous-time; Differential equations; Large-scale systems; Lyapunov method; Stability; Sufficient conditions; Tellurium;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.1980.1102356

Filename

1102356