Abstract:
l of dynamic objects is the development of methods for research
and synthesis of control systems of multidimensional objects.
The paper proposes a universal approach to construct
Lyapunov vector functions directly from the equation of state of
control system and a new gradient-speed method of Lyapunov
vector functions to study aperiodic robust stability of linear control system with m inputs and n outputs.
The study of aperiodic robust stability of automatic control
systems is based on the construction of Lyapunov vector functions and gradient-speed dynamic control systems.
The basic statements of Lyapunov’s theorem about asymptotic stability and notions of stability of dynamic systems are
used. The representation of control systems as gradient systems
and Lyapunov functions as potential functions of gradient systems from the catastrophe theory allow to construct the full-time
derivative of Lyapunov vector functions always as a sign-negative function equal to the scalar product of the velocity vector on
the gradient vector. The conditions of aperiodic robust stability
are obtained as a system of inequalities on the uncertain parameters of the automatic control system, which are a condition for
the existence of the Lyapunov vector-function.
A numerical example of synthesis of aperiodic robustness of
a multidimensional control object is given. The example shows
the main stages of the developed synthesis method, the study of
the system stability at different values of the coefficients k, confirming the consistency of the proposed method. Transients in
the system satisfy all requirements
