In the closed quantum system, if the control system is strongly regular and all other eigenstates are directly coupled to the target state, the control system can be asymptotically stabilized at the target eigenstate by the Lyapunov control based on the state error. However, if the control system is not strongly regular or as long as there is one eigenstate not directly coupled to the target st...

Low-rank iterative methods of periodic projected Lyapunov equations and their application in model reduction of periodic descriptor systems Low-rank iterative methods of periodic projected Lyapunov equations and their application in model reduction of periodic descriptor systems Abstract We discuss the numerical solution of large-scale sparse projected discrete-time periodic Lyapunov equations ...

A method for the explicit computation of the Lyapunov exponents of certain Markov processes is developed. Its utility is demonstrated by an application to two-dimensional random evolution differential equations. Our approach exploits the relation between the Lyapunov exponent and the p-moment Lyapunov exponents, as was first observed and studied by Arnold [1]. The p-moment Lyapunov exponent is ...

In Robust control design of nonlinear uncertain systems, stability theory plays an important role in engineering systems. For any given control system, it is crucial to have a stable system since an unstable control system is useless. Lyapunov . stability criterion is a general and useful procedure for studying the stability of nonlinear systems. The Lyapunov stability theory include two method...

We present a straightforward and reliable continuous method for computing the full or a partial Lyapunov spectrum associated with a dynamical system specified by a set of differential equations. We do this by introducing a stability parameter β > 0 and augmenting the dynamical system with an orthonormal k-dimensional frame and a Lyapunov vector such that the frame is continuously Gram-Schmidt o...