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This paper discusses and analyzes the capabilities and limitations of a series of related controllers for Euler-Bernoulli beam vibration, and the powerful capabilities of a robust second order sliding mode backstepping control method are exhibited. Motivated by the open-loop unstable response to harmonic excitations at resonant frequencies, specific attention is given to disturbances at system resonant frequencies. It is shown that the second order sliding mode backstepping controller provides arbitrary exponential stability of the beam position where other similar controllers cannot. Furthermore, it is shown that other controllers exhibit large (relative to the disturbance) steady state harmonic vibrations, or otherwise do not return the system to the origin. This paper is an extension of the Dynamic Systems and Control Division Vibrations Technical Committee “Best Vibrations Paper Award”-winning conference paper [1]. The previous work is significantly extended to include an exponentially stabilizing, second order sliding mode controller, and discusses several boundary conditions.

In this paper we have performed system analysis of target-mediated drug disposition (TDMM) models and study their stability, steady state (long term) behavior, and complexity. The original one- and two- compartment models are represented by systems of nonlinear differential equations. It has been found that these models are unstable at three different sets of their steady state values, which limits their applicability only to short time intervals. As an extension of the two-compartment TMDD model, the quasi-equilibrium model (QE-TMDD) appear to be very complex since it is represented by the system of differential-algebraic equations. Similar conclusion holds for its variant known as the quasi-steady state QSS-TMDD model. Moreover, it was shown analytically that when the initial value of the drug-receptor complex is zero, both QE-TMDD and QSS-TMDD models produce the zero values for the drug-receptor complex at all times, which appear to be a serious drawback for the applicability of these models.

In this article, we present simple alternative derivations for efficient evaluation of a matrix integral that has applications in optimal control and filtering, stability, controllability, observability, and controller design of linear time-invariant systems. The quadratic matrix integral (functional) is computed in terms of solutions of a sequence of algebraic Lyapunov equations. We present also a method to efficiently solve the obtained sequence of algebraic Lyapunov equations.

In this paper we show how to separate the slow and fast dynamics of the disparity convergence of the eye movements dynamic model. The dynamic equations obtained determine the modified slow dynamics that takes into account the impact of the fast dynamics and the modified fast dynamics that takes into account the impact of the slow dynamics. The slow fast decoupling is achieved by finding analytical solutions of the transformation equations used. The transformed slow and fast subsystems have very simple forms. Having separated the slow and fast dynamics completely, neural control problems for the slow and fast eye movements dynamics can be independently studied and better understood.In this paper we show how to separate the slow and fast dynamics of the disparity convergence of the eye movements dynamic model. The dynamic equations obtained determine the modified slow dynamics that takes into account the impact of the fast dynamics and the modified fast dynamics that takes into account the impact of the slow dynamics. The slow fast decoupling is achieved by finding analytical solutions of the transformation equations used. The transformed slow and fast subsystems have very simple forms. Having separated the slow and fast dynamics completely, neural control problems for the slow and fast eye movements dynamics can be independently studied and better understood.