Abstract
The paper describes novel necessary and sufficient conditions for stability study of nonautonomous dynamical systems. The necessary conditions establish the existence of a surface through which the flow of the vector field has a given sign. The relation between the proposed necessary conditions with the integral and differential forms of continuity equations is shown. The sufficient condition establishes uniform stability and uniform asymptotic stability of a system equilibrium point using some properties of the vector field divergence. The proposed sufficient conditions are applied to design the state feedback control laws. The control law is found as a solution of a partial differential inequality, whereas the control law based on Lyapunov method is a solution of algebraic inequality. The examples illustrate the efficiency of the proposed method compared with some existing ones.
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