Consideration was given to an autonomous model containing coupled subsystems (MCCS) and, in the absence of couplings between the subsystems, falling down into systems of ordinary differential equations. It is assumed that the subsystems admit different types of nondegenerate single-frequency oscillations. Solved were the problems of oscillations in MCCS, their stability, and stabilization of MCCS oscillation by smooth autonomous coupling controls. It was shown how the developed theory is applied to the coupled Duffing and Van der Pol oscillators.

Abstract|We consider the set of control points in a discrete device where testing is organized in groups with a signature analyzer. We solve the localization problem for a fault of any multiplicity located in one or different groups. For this purpose, in addition we construct various partitions of the set of control points where we organize similar group testing. We show an algorithm for constructing additional partitions. We solve the minimization problem for the testing hardware needed to implement it.

Nonlinear single-input affine systems represented in a canonical (normal) form are considered. The control resource is assumed to be constrained. For a closed-loop system obtained by applying a linearizing feedback, the problem of finding an estimate of the attraction domain is set. A method for constructing an ellipsoidal estimate that is based on results of absolute stability theory is suggested. Construction of the estimate reduces to solving a system of linear matrix inequalities. The discussion is illustrated by numerical examples.

The analysis of asymptotic stability of nonlinear oscillator is one of the classical problems in the theory of oscillations. Usually, it is solved by exploiting Lyapunov functions having the meaning of the full energy of the system. However, the Barbashin–Krasovskii theorem has to be used along this way, and no estimates can be found for the rate of convergence of the trajectories to equilibria points. In this paper we propose a different Lyapunov function which lacks transparent physical meaning. With this function, both the rate of convergence and the domain of attraction of equilibria points can be estimated. This result also enables an efficient analysis of another problem, synchronization of oscillations of two oscillators. We formulate conditions that guarantee frequency synchronization and, on top of that, phase synchronization. Generalizations to the case of arbitrary number of oscillators are also discussed; solution of this problem is crucial in the analysis of power systems.

We consider stabilization of bilinear control systems by means of linear output dynamical controllers. Using the linear matrix inequality technique, quadratic Lyapunov functions, and a special iterative method, we propose a regular approach to the construction of the stabilizability ellipsoid having the property that the trajectories of the system emanating from the points of this ellipsoid asymptotically tend to zero. The developed approach enables for an efficient construction of nonconvex inner approximations of domains of stabilizability of bilinear control systems.