New sufficient conditions for the oscillation of all solutions to a class of third-order Emden–Fowler differential equations with unbounded neutral coefficients are established. The criteria obtained ...essentially improve related results in the literature. In particular, as opposed to known results, new criteria can distinguish solutions of third-order differential equations with different behaviors. Examples are also provided to illustrate the results.
In the paper, new single-condition criteria for the oscillation of all solutions to a second-order half-linear delay differential equation in noncanonical form are obtained, relaxing a traditionally ...posed assumption that the delay function is nondecreasing. The oscillation constant is best possible in the sense that the strict inequality cannot be replaced by the nonstrict one without affecting the validity of the theorem. This sharp result is new even in the linear case and, to the best of our knowledge, improves all the existing results reporting in the literature so far. The advantage of our approach is the simplicity of the proof, only based on sequentially improved monotonicities of a positive solution.
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DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, UILJ, UKNU, UL, UM, UPUK
In this study, we consider parameter‐dependent diffusion eigenvalue problem on time scales. An upper bound on the number of eigenvalues for this problem on a finite time scale is given.
The paper is devoted to the study of oscillation of solutions to a class of second-order half-linear neutral differential equations with delayed arguments. New oscillation criteria are established, ...and they essentially improve the well-known results reported in the literature, including those for non-neutral differential equations. The adopted approach refines the classical Riccati transformation technique by taking into account such part of the overall impact of the delay that has been neglected in the earlier results. The effectiveness of the obtained criteria is illustrated via examples.
This paper is a continuation of the recent study by Bohner et al 9 on oscillation properties of nonlinear third order functional differential equation under the assumption that the second order ...differential equation is nonoscillatory. We consider both the delayed and advanced case of the studied equation. The presented results correct and extend earlier ones. Several illustrative examples are included.
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DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, UILJ, UKNU, UL, UM, UPUK
Research in the field of underactuated systems shows that control algorithms which take the natural dynamics of the system’s underactuated part into account are more energy-efficient than those ...utilizing fully-actuated systems. The purpose of this paper to apply the two-degrees-of-freedom (feedforward/feedback) control structure to design a swing-up manoeuver that involves tracking the desired trajectories so as to achieve and maintain the unstable equilibrium position of the pendulum on the cart system. The desired trajectories are obtained by solving the boundary value problem of the internal system dynamics, while the optimal state-feedback controller ensures that the desired trajectory is tracked with minimal deviations. The proposed algorithm is verified on the simulation model of the available laboratory model actuated by a linear synchronous motor, and the resulting program implementation is used to enhance the custom Simulink library Inverted Pendula Modeling and Control, developed by the authors of this paper.
The aim of the present paper is to continue earlier works by the
authors on the oscillation problem of second-order half-linear neutral
delay differential equations. By revising the set method, we ...present new
oscillation criteria which essentially improve a number of related ones
from the literature. A couple of examples illustrate the value of the
results obtained.
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Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, UILJ, UKNU, UL, UM, UPUK
The purpose of this paper is to present an in-depth survey of the rotary single inverted pendulum system from a control engineer's point of view. The scope of the survey includes modeling and ...open-loop analysis of the system as well as design and verification of balancing and swing up controllers which ensure successful stabilization of the pendulum in the unstable upright equilibrium. All relevant tasks and simulation experiments are conducted using the appropriate function blocks, GUI applications and demonstration schemes from a Simulink block library developed by the authors of the paper. The library is called Inverted Pendula Modeling and Control (IPMaC) and offers comprehensive program support for modeling, simulation and control of classical (linear) and rotary inverted pendulum systems.
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