In this paper, a bias-compensated least squares (BCLS) method in the closed loop environment is proposed. It is assumed that the observation noise is a white gaussinan signal while there are no process noises. It is also assumed that the plant is controlled by a linear time invariant controller and that the closed loop system is asymptotically stable. The proposed estimator is unbiased and it d...

The computation of Lyapunov quantities is closely connected with the important in engineering mechanics question of dynamical system behavior near to boundary of the stability domain. Followed by the work of Bautin [1], one differs "safe" or "dangerous" boundaries, a slight shift of which implies a small (invertible) or noninvertible changes of system status, respectively. Such changes correspo...

In this paper, a nonlinear discrete-time system in the presence of input disturbance and measurement noise is approximated by subsystems described by the linear pulse-transfer functions with the subjection of input disturbance and measurement noise. Although the input disturbance and the measurement noise are unknown, they are modeled as known pulse-transfer functions. The approximation error b...

In this paper, we describe in detail a method of computing Lyapunov exponents for a continuous-time dynamical system and extend the method to discrete maps. Using this method, a partial Lyapunov spectrum can be computed using fewer equations as compared to the computation of the full spectrum, there is no difficulty in evaluating degenerate Lyapunov spectra, the equations are straightforward to...

In this article, we consider chaotic behavior happened in nonsmooth dynamical systems. To quantify such a behavior, a computation of Lyapunov exponents for chaotic orbits of a given nonsmooth dynamical system is focused. The Lyapunov exponent is a very important concept in chaotic theory, because this quantity measures the sensitive dependence on initial conditions in dynamical systems. Therefo...

We develop a direct Lyapunov method for the almost sure open-loop stabilizability and asymptotic stabilizability of controlled degenerate diffusion processes. The infinitesimal decrease condition for a Lyapunov function is a new form of Hamilton-Jacobi-Bellman partial differential inequality of 2nd order. We give local and global versions of the First and Second Lyapunov Theorems assuming the e...

The computation of the entire Lyapunov spectrum for extended dynamical systems is a very time consuming task. If the system is in a chaotic spatio-temporal regime it is possible to approximately reconstruct the Lyapunov spectrum from the spectrum of a subsystem by a suitable rescaling in a very cost effective way. We compute the Lyapunov spectrum for the subsystem by truncating the original Jac...