On global linearization of planar involutions

Let phi: a"e(2) -> a"e(2) be an orientation-preserving C (1) involution such that phi(0) = 0. Let Spc(phi) = {Eigenvalues of D phi(p) | p a a"e(2)}. We prove that if Spc(phi) aS, a"e or Spc(phi) a (c) [1, 1 + epsilon) = a... for some epsilon > 0, then phi is globally C (1) conjugate to the linear involution D phi(0) via the conjugacy h = (I + D phi(0)phi)/2,where I: a"e(2) -> a"e(2) is the identity map. Similarly, we prove that if phi is an orientation-reversing C (1) involution such that phi(0) = 0 and Trace (D phi(0)D phi(p) > - 1 for all p a a"e(2), then phi is globally C (1) conjugate to the linear involution D phi(0) via the conjugacy h. Finally, we show that h may fail to be a global linearization of phi if the above conditions are not fulfilled.

Practical stability of approximating discrete-time filters with respect to model mismatch

This paper establishes practical stability results for an important range of approximate discrete-time filtering problems involving mismatch between the true system and the approximating filter model. Practical stability is established in the sense of an asymptotic bound on the amount of bias introduced by the model approximation. Our analysis applies to a wide range of estimation problems and justifies the common practice of approximating intractable infinite dimensional nonlinear filters by simpler computationally tractable filters.

Non-linear resonance in strings under narrow band random excitation, part I: Planar response and stability

Non-linear planar response of a string to planar narrow band random excitation is investigated in this paper. A response equation for the mean square deflection σ2 is obtained under a single mode approximation by using the equivalent linearization technique. It is shown that the response is triple valued, as in the case of harmonic excitation, if the centre frequency of excitation Ω lies in a certain specified range. The triple valued response occurs only if the excitation bandwidth β is smaller than a critical value βcrit which is a monotonically increasing function of the intensity of excitation. An approximate method of investigating the almost sure asymptotic stability of the solution is presented and regions of instability in the Ω-σ2 plane have been charted. It is shown that planar response can become unstable either due to an unbounded growth of the in-plane component of motion or due to a spontaneous appearance of an out-of-plane component.

Dissipativeness and Stability of a Class of Distributed Parameter Systems

Input-output stability of linear-distributed parameter systems of arbitrary order and type in the presence of a distributed controller is analyzed by extending the concept of dissipativeness, with certain modifications, to such systems. The approach is applicable to systems with homogeneous or homogenizable boundary conditions. It also helps in generating a Liapunov functional to assess asymptotic stability of the system.

Stability of scheduled multi-access communication over quasi-static flat fading channels with random coding and independent decoding

The stability of scheduled multiaccess communication with random coding and independent decoding of messages is investigated. The number of messages that may be scheduled for simultaneous transmission is limited to a given maximum value, and the channels from transmitters to receiver are quasistatic, flat, and have independent fades. Requests for message transmissions are assumed to arrive according to an i.i.d. arrival process. Then, we show the following: (1) in the limit of large message alphabet size, the stability region has an interference limited information-theoretic capacity interpretation, (2) state-independent scheduling policies achieve this asymptotic stability region, and (3) in the asymptotic limit corresponding to immediate access, the stability region for non-idling scheduling policies is shown to be identical irrespective of received signal powers.

Stability of systems with power-law non-linearities

It is shown that a sufficient condition for the asymptotic stability-in-the-large of an autonomous system containing a linear part with transfer function G(jω) and a non-linearity belonging to a class of power-law non-linearities with slope restriction [0, K] in cascade in a negative feedback loop is ReZ(jω)[G(jω) + 1 K] ≥ 0 for all ω where the multiplier is given by, Z(jω) = 1 + αjω + Y(jω) - Y(-jω) with a real, y(t) = 0 for t < 0 and ∫ 0 ∞ |y(t)|dt < 1 2c2, c2 being a constant associated with the class of non-linearity. Any allowable multiplier can be converted to the above form and this form leads to lesser restrictions on the parameters in many cases. Criteria for the case of odd monotonic non-linearities and of linear gains are obtained as limiting cases of the criterion developed. A striking feature of the present result is that in the linear case it reduces to the necessary and sufficient conditions corresponding to the Nyquist criterion. An inequality of the type |R(T) - R(- T)| ≤ 2c2R(0) where R(T) is the input-output cross-correlation function of the non-linearity, is used in deriving the results.

Optimal infinite-horizon feedback laws for a general class of constrained discrete-time systems: stability and moving-horizon approximations

Stability results are given for a class of feedback systems arising from the regulation of time-varying discrete-time systems using optimal infinite-horizon and moving-horizon feedback laws. The class is characterized by joint constraints on the state and the control, a general nonlinear cost function and nonlinear equations of motion possessing two special properties. It is shown that weak conditions on the cost function and the constraints are sufficient to guarantee uniform asymptotic stability of both the optimal infinite-horizon and movinghorizon feedback systems. The infinite-horizon cost associated with the moving-horizon feedback law approaches the optimal infinite-horizon cost as the moving horizon is extended.

About the Stabilization of a Nonlinear Perturbed Difference Equation

This paper investigates the local asymptotic stabilization of a very general class of instable autonomous nonlinear difference equations which are subject to perturbed dynamics which can have a different order than that of the nominal difference equation. In the general case, the controller consists of two combined parts, namely, the feedback nominal controller which stabilizes the nominal (i.e., perturbation-free) difference equation plus an incremental controller which completes the stabilization in the presence of perturbed or unmodeled dynamics in the uncontrolled difference equation. A stabilization variant consists of using a single controller to stabilize both the nominal difference equation and also the perturbed one under a small-type characterization of the perturbed dynamics. The study is based on Banach fixed point principle, and it is also valid with slight modification for the stabilization of unstable oscillatory solutions.

A robust position control for induction machines

ICEM 2010

Existence, uniqueness, and stability of solutions of a class of nonlinear partial differential equations

In this study we investigate the existence, uniqueness and asymptotic stability of solutions of a class of nonlinear integral equations which are representations for some time dependent non- linear partial differential equations. Sufficient conditions are established which allow one to infer the stability of the nonlinear equations from the stability of the linearized equations. Improved estimates of the domain of stability are obtained using a Liapunov Functional approach. These results are applied to some nonlinear partial differential equations governing the behavior of nonlinear continuous dynamical systems.

Stability of parametrically excited differential equations

Sufficient stability criteria for classes of parametrically excited differential equations are developed and applied to example problems of a dynamical nature.

Stability requirements are presented in terms of 1) the modulus of the amplitude of the parametric terms, 2) the modulus of the integral of the parametric terms and 3) the modulus of the derivative of the parametric terms.

The methods employed to show stability are Liapunov’s Direct Method and the Gronwall Lemma. The type of stability is generally referred to as asymptotic stability in the sense of Liapunov.

The results indicate that if the equation of the system with the parametric terms set equal to zero exhibits stability and possesses bounded operators, then the system will be stable under sufficiently small modulus of the parametric terms or sufficiently small modulus of the integral of the parametric terms (high frequency). On the other hand, if the equation of the system exhibits individual stability for all values that the parameter assumes in the time interval, then the actual system will be stable under sufficiently small modulus of the derivative of the parametric terms (slowly varying).

Global analysis of mRNA half-lives and de novo transcription in a dinoflagellate, Karenia brevis

Dinoflagellates possess many physiological processes that appear to be under post-transcriptional control. However, the extent to which their genes are regulated post-transcriptionally remains unresolved. To gain insight into the roles of differential mRNA stability and de novo transcription in dinoflagellates, we biosynthetically labeled RNA with 4-thiouracil to isolate newly transcribed and pre-existing RNA pools in Karenia brevis. These isolated fractions were then used for analysis of global mRNA stability and de novo transcription by hybridization to a K. brevis microarray. Global K. brevis mRNA half-lives were calculated from the ratio of newly transcribed to pre-existing RNA for 7086 array features using the online software HALO (Half-life Organizer). Overall, mRNA half-lives were substantially longer than reported in other organisms studied at the global level, ranging from 42 minutes to greater than 144 h, with a median of 33 hours. Consistent with well-documented trends observed in other organisms, housekeeping processes, including energy metabolism and transport, were significantly enriched in the most highly stable messages. Shorter-lived transcripts included a higher proportion of transcriptional regulation, stress response, and other response/regulatory processes. One such family of proteins involved in post-transcriptional regulation in chloroplasts and mitochondria, the pentatricopeptide repeat (PPR) proteins, had dramatically shorter half-lives when compared to the arrayed transcriptome. As transcript abundances for PPR proteins were previously observed to rapidly increase in response to nutrient addition, we queried the newly synthesized RNA pools at 1 and 4 h following nitrate addition to N-depleted cultures. Transcriptome-wide there was little evidence of increases in the rate of de novo transcription during the first 4 h, relative to that in N-depleted cells, and no evidence for increased PPR protein transcription. These results lend support to the growing consensus of post-transcriptional control of gene expression in dinoflagellates.

Global state synchronization in networks of cyclic feedback systems

This technical note studies global asymptotic state synchronization in networks of identical systems. Conditions on the coupling strength required for the synchronization of nodes having a cyclic feedback structure are deduced using incremental dissipativity theory. The method takes advantage of the incremental passivity properties of the constituent subsystems of the network nodes to reformulate the synchronization problem as one of achieving incremental passivity by coupling. The method can be used in the framework of contraction theory to constructively build a contracting metric for the incremental system. The result is illustrated for a network of biochemical oscillators. © 2011 IEEE.

De lo micro a lo macro prudencial: Un análisis de la supervisión bancaria desde la econometría espacial

La crisis que se desató en el mercado hipotecario en Estados Unidos en 2008 y que logró propagarse a lo largo de todo sistema financiero, dejó en evidencia el nivel de interconexión que actualmente existe entre las entidades del sector y sus relaciones con el sector productivo, dejando en evidencia la necesidad de identificar y caracterizar el riesgo sistémico inherente al sistema, para que de esta forma las entidades reguladoras busquen una estabilidad tanto individual, como del sistema en general. El presente documento muestra, a través de un modelo que combina el poder informativo de las redes y su adecuación a un modelo espacial auto regresivo (tipo panel), la importancia de incorporar al enfoque micro-prudencial (propuesto en Basilea II), una variable que capture el efecto de estar conectado con otras entidades, realizando así un análisis macro-prudencial (propuesto en Basilea III).

An algebraic approach for delay-independent and delay-dependent stability of linear time-delay systems

This paper addresses the problem of asymptotic stability of a linear system with many delay units. A novel algebraic test is proposed for the delay-independent stability of the system, based on the root distribution of the system's characteristic equation. If the system is only stable dependent of delay, the whole stable regions of the system can be perfectly obtained. Two algorithms are derived to examine the delay-independent stability, and to compute the whole stable regions if the system is of delay-dependent stability. These algorithms are computationally efficient and applicable to both certain and uncertain systems. Some illustrative examples demonstrate the validity of the approach.