7,116 research outputs found
Hyers-Ulam-Rassias Stability of Functional Differential Systems with Point and Distributed Delays
This paper investigates stability and asymptotic properties of the error with respect to its nominal version of a nonlinear time-varying perturbed functional differential system subject to point, finite-distributed, and Volterra-type distributed delays associated with linear dynamics together with a class of nonlinear delayed dynamics. The boundedness of the error and its asymptotic convergence to zero are investigated with the results being obtained based on the Hyers-Ulam-Rassias analysis
A note on the continuability of solutions of a perturbed second order nonlinear differential equation of lienard type
In this note we study the continuability of the solutions of a Liénard type equation with forcing term under suitable assumptions.Fil: Napoles Valdes, Juan Eduardo. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura. Departamento de Matemática; ArgentinaFil: Lugo, Luciano Miguel. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura. Departamento de Matemática; ArgentinaFil: Guzmán, Paulo Matias. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin
On the boundedness of some nonlinear differential equation of second order
In this paper we study the boundedness of the solutions of some nonlinear dofferential equation using as a key tool the Second Lyapunov method, i.e. find sufficient conditions under which the solutions of this equation are bounded. Variuos particular cases and methodological remarks are included at the end of paper.Fil: Guzmán, Paulo Matias. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Napoles Valdes, Juan Eduardo. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura. Departamento de Matemática; ArgentinaFil: Lugo, Luciano Miguel. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura. Departamento de Matemática; Argentin
Uniform semiglobal practical asymptotic stability for non-autonomous cascaded systems and applications
It is due to the modularity of the analysis that results for cascaded systems
have proved their utility in numerous control applications as well as in the
development of general control techniques based on ``adding integrators''.
Nevertheless, the standing assumptions in most of the present literature on
cascaded systems is that, when decoupled, the subsystems constituting the
cascade are uniformly globally asymptotically stable (UGAS). Hence existing
results fail in the more general case when the subsystems are uniformly
semiglobally practically asymptotically stable (USPAS). This situation is often
encountered in control practice, e.g., in control of physical systems with
external perturbations, measurement noise, unmodelled dynamics, etc. This paper
generalizes previous results for cascades by establishing that, under a uniform
boundedness condition, the cascade of two USPAS systems remains USPAS. An
analogous result can be derived for USAS systems in cascade. Furthermore, we
show the utility of our results in the PID control of mechanical systems
considering the dynamics of the DC motors.Comment: 16 pages. Modifications 1st Feb. 2006: additional requirement that
links the parameter-dependency of the lower and upper bounds on the Lyapunov
function, stronger condition of uniform boundedness of solutions,
modification and simplification of the proofs accordingl
Ultimate boundedness of droop controlled Microgrids with secondary loops
In this paper we study theoretical properties of inverter-based microgrids
controlled via primary and secondary loops. Stability of these microgrids has
been the subject of a number of recent studies. Conventional approaches based
on standard hierarchical control rely on time-scale separation between primary
and secondary control loops to show local stability of equilibria. In this
paper we show that (i) frequency regulation can be ensured without assuming
time-scale separation and, (ii) ultimate boundedness of the trajectories
starting inside a region of the state space can be guaranteed under a condition
on the inverters power injection errors. The trajectory ultimate bound can be
computed by simple iterations of a nonlinear mapping and provides a certificate
of the overall performance of the controlled microgrid.Comment: 8 pages, 1 figur
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