Abstract

We investigate a new approach to the construction of vector Lyapunov functions. An approach to the construction of Lyapunov functions as vector functions is developed based on a geometrical interpretation of the second method of Lyapunov. The negative of the gradient is determined from the components of the time derivative of the state vector (i.e., the right-hand side of the state equation). The region of stability of a closed-loop linear, stationary system with uncertain parameters is governed by inequalities in the matrix elements of the closed-loop system. This study developed a method for analysing the robust stability of SISO and MIMO linear systems in canonical forms.

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