Stability/instability study of density systems and control law design

Abstract

The paper considers some class of dynamical systems that called density systems. For such systems the derivative of quadratic function depends on so-called density function. The density function is used to set the properties of phase space, therefore, it influences the behaviour of investigated systems. A particular class of such systems is previously considered for (in)stability study of dynamical systems using the flow and divergence of a phase vector. In this paper, a more general class of such systems is considered, and it is shown that the density function can be used not only to study (in)stability, but also to set the properties of space in order to change the behaviour of dynamical systems. The development of control laws based on use the density function for systems with known and unknown parameters is considered. All obtained results are accompanied by the simulations illustrating the theoretical conclusions.