Control system analysis and design upon the Lyapunov method

The objectives of the present paper are analysis of stability of the nonlinear continuous-time systems and application of the second method to the optimization problem. Based on Lyapunov's method and the Hamilton-Jacobi-Bellman theory we outline procedures which can be used to unify results in stability analysis and system design. For nonlinear time-varying dynamical systems we show how the nonlinear optimization problem can be solved. Four illustrative examples are considered in details to demonstrate the advantages of the given analysis and control methodologies.