Oscillations of power systems cause instability in power networks. Power system stabilizer (PSS) is used as a conventional method to damp these oscillations . Finding the optimized gain of PSS is one of the major problems in power system stability issue. In this paper, single machine connected to an infinite bus and 10-machines 39-bus network are considered for study. it's shown that finding th...

A new direct method for the computation of Lyapunov quantities (Lyapunov values or coefficients, Poincare-Lyapunov constants, focus values) for the second-order dynamical system, permitting us to narrow the requirements on a smoothness of system, is obtained.

In this paper, an iterative technique is proposed to solve linear integrated active/passive design problems. The optimality of active and passive parts leads to the nonlinear algebraic Riccati equation due to the active parameters and some associated additional Lyapunov equations due to the passive parameters. Rather than the solution of the nonlinear algebraic Riccati equation, it is proposed ...

The paper deals with the problem of estimation of the topological entropy for non-autonomous systems of differential equations via the second (direct) Lyapunov method. The main result of the paper is illustrated by examples concerning the Lorenz system and Duffing oscillator.

The problem of robust adaptive stabilization of a class of multi-input multi-output nonlinear systems with constant linearly parameterized uncertainty and unknown structure of bounded variation have been considered. With the aid of direct adaptive technique and control Lyapunov function method, a robust adaptive controller is designed to complete the globally adaptive stability of the closed-lo...

We consider linear matrix equations where the linear mapping is the sum of a standard Lyapunov operator and a positive operator. These equations play a role in the context of stochastic or bilinear control systems. To solve them efficiently one can fall back on known efficient methods developed for standard Lyapunov equations. In the present paper we describe a direct and an iterative method ba...

In this paper, we investigate the leader-following based formation control of nonholonomic mobile robots. We present a new kinematics model for the leader-follower system using Cartesian coordinates. Based on this new model and the direct Lyapunov method, a globally stable controller is derived for the whole system. Simulation results are included to verify the feasibility of the proposed model...