In this paper, we present a robust H∞ observer for a class of nonlinear and uncertain time-delayed systems. To design the proposed observer, the time delay does not have to be exactly known. With knowledge about upper and lower bound of the delay term, we can design an H∞ observer that guarantees asymptotic stability of the estimation error dynamics and is robust against time-varying parametric uncertainties. We show that the described problem can be solved in terms of linear matrix inequalities (LMIs). In addition, the admissible Lipschitz constant of the system is maximized and the disturbance attenuation level is minimized through convex multi-objective optimization. Finally, the proposed observer is illustrated with an example.

 In this article the problem of characterizing sets, described by vector nonlinear inequalities of the form $v(x)leq w,$ as robustly positively invariant and targets of uniformly ultimate bounded nonlinear systems is investigated. The class of general parameter uncertain continuous-time dynamical systems affected by exogenous disturbances is considered. The approach is based on establishing an associated monotone nonlinear comparison system. A numerical example is presented to illustrate the approach.

 This paper describes a parameter estimation algorithm applicable for the model structures in the form of multivariate polynomial systems. An example of a synchronous machine nonlinear model is used throughout the paper to explain the contribution. The fundamental in the proposed algorithm is the idea of reformulating the least squares estimation problem having the polynomial model into a numerical linear algebra problem. Recorded signals are represented using the Lagrange interpolation at the Chebyshev points which allows accurate computation of signal derivatives and numerical integration as both are required in the algorithm. The paper explores sensitivity of the algorithm to the power of recorded signals (i.e. excitation intensity) and discusses impact of roundoff error.

 The main purpose of this study is the description of the qualitative dynamical response of a rotary drilling system with a drag bit, using a model that takes into consideration the axial and the torsional vibration modes of the bit. The studied model, based on the interface bit-rock, contains a couple of wave equations with boundary conditions consisting of the angular speed and the axial speed at the top additionally to the angular and axial acceleration at the bit whose contain a realistic frictional torque. Our analysis is based on the center manifold Theorem and Normal forms theory whose allow us to simplify the model.

Index Terms: Drilling system, Vibrations analysis, Time-Delay Systems, Neutral systems, Functional differential equations, Center Manifold, Normal forms.

 This paper presents funnel control for position control of rigid, revolute joint, n-degree-of-freedom (DOF) robotic manipulators with known inertia matrix. The multi- input multi-output (MIMO) funnel controller assures reference tracking with prescribed transient accuracy, i.e., for each joint, the absolute value of position and speed tracking error (difference between reference and actual value) is bounded by a prescribed, positive (possibly non-increasing) function of time (the funnel boundary), respectively.