Improved Conditions For L2-Stability Of Nonstationary Feedback-Systems

Concerning the L2-stability of feedback systems containing a linear time-varying operator, some of the stringent restrictions imposed on the multiplier as well as the linear part of the system, in the criteria presented earlier, are relaxed.

L2-Stability Of A Class Of Nonlinear-Systems

Sufficient conditions are given for the L2-stability of a class of feedback systems consisting of a linear operator G and a nonlinear gain function, either odd monotone or restricted by a power-law, in cascade, in a negative feedback loop. The criterion takes the form of a frequency-domain inequality, Re[1 + Z(jω)] G(jω) δ > 0 ω ε (−∞, +∞), where Z(jω) is given by, Z(jω) = β[Y1(jω) + Y2(jω)] + (1 − β)[Y3(jω) − Y3(−jω)], with 0 β 1 and the functions y1(·), y2(·) and y3(·) satisfying the time-domain inequalities, ∝−∞+∞¦y1(t) + y2(t)¦ dt 1 − ε, y1(·) = 0, t < 0, y2(·) = 0, t > 0 and ε > 0, and , c2 being a constant depending on the order of the power-law restricting the nonlinear function. The criterion is derived using Zames' passive operator theory and is shown to be more general than the existing criteria

Time-Domain Criteria For L2-Stability Of Nonstationary Feedback-Systems

Criteria for the L2-stability of linear and nonlinear time-varying feedback systems are given. These are conditions in the time domain involving the solution of certain associated matrix Riccati equations and permitting the use of a very general class of L2-operators as multipliers.

Optimum Design for External Seismic Stability of Geosynthetic Reinforced Soil Walls: Reliability Based Approach

In this paper, an analytical study considering the effect of uncertainties in the seismic analysis of geosynthetic-reinforced soil (GRS) walls is presented. Using limit equilibrium method and assuming sliding wedge failure mechanism, analysis is conducted to evaluate the external stability of GRS walls when subjected to earthquake loads. Target reliability based approach is used to estimate the probability of failure in three modes of failure, viz., sliding, bearing, and eccentricity failure. The properties of reinforced backfill, retained backfill, foundation soil, and geosynthetic reinforcement are treated as random variables. In addition, the uncertainties associated with horizontal seismic acceleration and surcharge load acting on the wall are considered. The optimum length of reinforcement needed to maintain the stability against three modes of failure by targeting various component and system reliability indices is obtained. Studies have also been made to study the influence of various parameters on the seismic stability in three failure modes. The results are compared with those given by first-order second moment method and Monte Carlo simulation methods. In the illustrative example, external stability of the two walls, Gould and Valencia walls, subjected to Northridge earthquake is reexamined.

Structural stability of slender aerospace vehicles: Part I Mathematical modeling

A detailed mechanics based model is developed to analyze the problem of structural instability in slender aerospace vehicles. Coupling among the rigid-body modes, the longitudinal vibrational modes and the transverse vibrational modes due to asymmetric lifting-body cross-section are considered. The model also incorporates the effects of aerodynamic pressure and the propulsive thrust of the vehicle. The model is one-dimensional, and it can be employed to idealized slender vehicles with complex shapes. Condition under which a flexible body with internal stress waves behaves like a perfect rigid body is derived. Two methods are developed for finite element discretization of the system: (1) A time-frequency Fourier spectral finite element method and (2) h-p finite element method. Numerical results using the above methods are presented in Part II of this paper. (C) 2010 Elsevier Ltd. All rights reserved.

Optimum Design for External Seismic Stability of Geosynthetic Reinforced Soil Walls: Reliability Based Approach

In this paper, an analytical study considering the effect of uncertainties in the seismic analysis of geosynthetic-reinforced soil (GRS) walls is presented. Using limit equilibrium method and assuming sliding wedge failure mechanism, analysis is conducted to evaluate the external stability of GRS walls when subjected to earthquake loads. Target reliability based approach is used to estimate the probability of failure in three modes of failure, viz., sliding, bearing, and eccentricity failure. The properties of reinforced backfill, retained backfill, foundation soil, and geosynthetic reinforcement are treated as random variables. In addition, the uncertainties associated with horizontal seismic acceleration and surcharge load acting on the wall are considered. The optimum length of reinforcement needed to maintain the stability against three modes of failure by targeting various component and system reliability indices is obtained. Studies have also been made to study the influence of various parameters on the seismic stability in three failure modes. The results are compared with those given by first-order second moment method and Monte Carlo simulation methods. In the illustrative example, external stability of the two walls, Gould and Valencia walls, subjected to Northridge earthquake is reexamined.

Stability of scheduled message communication over degraded broadcast channels

We develop a multi-class discrete-time processor-sharing queueing model for scheduled message communication over a discrete memoryless degraded broadcast channel. The framework we consider here models both the random message arrivals and the subsequent reliable communication by suitably combining techniques from queueing theory and information theory. Requests for message transmissions are assumed to arrive according to i.i.d. arrival processes. Then, (i) we derive an outer bound to the stability region of message arrival rate vectors achievable by the class of stationary scheduling policies, (ii) we show for any message arrival rate vector that satisfies the outer bound, that there exists a stationary "state-independent" policy that results in a stable system for the corresponding message arrival processes, and (iii) under an asymptotic regime, we show that the stability region of information arrival rate vectors is the information-theoretic capacity region of a degraded broadcast channel.

On the L2 stability of linear multidimensional time varying systems

This paper analyzes the L2 stability of solutions of systems with time-varying coefficients of the form [A + C(t)]x′ = [B + D(t)]x + u, where A, B, C, D are matrices. Following proof of a lemma, the main result is derived, according to which the system is L2 stable if the eigenvalues of the coefficient matrices are related in a simple way. A corollary of the theorem dealing with small periodic perturbations of constant coefficient systems is then proved. The paper concludes with two illustrative examples, both of which deal with the attitude dynamics of a rigid, axisymmetric, spinning satellite in an eccentric orbit, subject to gravity gradient torques.

Bounded-input/bounded-output stability of linear multidimensional time- varying systems

The present study of the stability of systems governed by a linear multidimensional time-varying equation, which are encountered in spacecraft dynamics, economics, demographics, and biological systems, gives attention the lemma dealing with L(inf) stability of an integral equation that results from the differential equation of the system under consideration. Using the proof of this lemma, the main result on L(inf) stability is derived according; a corollary of the theorem deals with constant coefficient systems perturbed by small periodic terms. (O.C.)

Role of aluminum-magnesium alloys in humid aging of composite solid propellants

The humid aging of composite propellants containing a terpolymer of polybutadiene, acrylic acid, and acrylonitrile (PBAN) as a binder has been studied as a function of aging temperature, relative humidity, and aging time. Three composite types - AP-PBAN, AP-Al-PBAN, and AP-(Al-Mg) alloy- PBAN - have been studied. The burning rates of all three propellant types were unaffected by aging. The calorimetric values of composites containing aluminum-magnesium alloy decreased on aging, and the lattice parameter of the alloy decreased to a value close to that of aluminum. Water absorption in all of the samples increased with increases in the temperature, relative humidity, and aging time. The compression strength of the nonmetalized and aluminized samples decreased on aging, whereas that of the composites containing the alloy increased. The latter effect has been traced to reaction of residual carboxyl groups on the polymer chains with magnesium, leading to cross-linking. The reaction between the -COOH groups and magnesium has been proved using infrared spectroscopy. (Author)

Stability of CU(2)Ln(2)O(5) compounds - Comparison, assessment and systematics

Phase diagram studies show that at ambient pressure only one ternary oxide, Cu(2)Ln(2)O(5), is stable in the ternary systems Cu-Ln-O (Ln = Tb, Dy, Ho, Er, Tm, Yb, Lu) at high temperatures. The crystal structure of Cu(2)Ln(2)O(5) can be described as a zig-zag arrangement of one-dimensional Cu2O5 chains parallel to-the a-axis with Ln atoms occupying distorted octahedral sites between these chains. Four sets of emf measurements on Gibbs energy of formation of Cu(2)Ln(2)O(5) (Ln = Tb, Dy, Ho, Er, Tm, Yb, Lu; Y) from component binary oxides and one set of high-temperature solution calorimetric data on enthalpy of formation have been reported in the literature. Except for Cu2Y2O5, the measured values for the Gibbs energies of formation of all other Cu(2)Ln(2)O(5) compounds fall in a narrow band (+/-1 kJ mol(-1)) and indicate a regular increase in stability with decreasing ionic radius of the lanthanide ion. The values for the second law enthalpy of formation, derived from the temperature dependence of emf obtained in different studies, show larger differences, as high as 25 kJ mol(-1) for Cu2Tm2O5. Though associated with an uncertainty of +/-4 kJ mol(-1), the calorimetric measurements help to identify the best set of emf data. The trends in thermodynamic data correlate well with the global instability index (GII) based on the overall deviation from the valence sum rule. Low values for the index calculated from crystallographic information indicate higher stability. Higher values are indicative of the larger stress in the structure.

Trends in the stability of ternary oxides: Systems M-Pb-O (M = Ca, Sr, Ba)

Recent experimental investigations of phase equilibria and thermodynamic properties of the systems M-Pb-O, where M = Ca, Sr or Ba, indicate a regular increase in thermodynamic stability of ternary oxides, MPbO3 and M2PbO4, with increasing basicity of the oxide of the alkaline-earth metal. Number of stable interoxide compounds at 1100 K in the systems M-Pb-O (M = Mg, Ca, Sr, Ba) increases in unit increments from Mg to Ba. In this paper, experimentally determined standard Gibbs energies of formation of M2PbO4 (M = Ca, Sr, Ba) and MPbO3 (M = Sr, Ba) from their component binary monoxides and oxygen gas are combined with an estimated value for CaPbO3 to delineate systematic trends in thermodynamic stability of the ternary oxides. The trends are interpreted using concepts of tolerance factor and acid-base interactions. All the ternary oxides in these systems contain lead in the tetravalent state. The small Pb4+ ions polarize the surrounding oxygen ions and cause the formation of oxyanions which are acidic in character. Hence, the higher oxidation state of lead is stabilized in the presence of basic oxides of alkaline-earth group. A schematic subsolidus temperature-composition phase diagram is presented for the system BaO-PbO-O-2 to illustrate the change in oxidation states in binary and ternary oxides with temperature.

Some recent results on the stability of linear time varying systems

Some theorems derived recently by the authors on the stability of multidimensional linear time varying systems are reported in this paper. To begin with, criteria based on Liapunov�s direct method are stated. These are followed by conditions on the asymptotic behaviour and boundedness of solutions. Finally,L 2 andL ? stabilities of these systems are discussed. In conclusion, mention is made of some of the problems in aerospace engineering to which these theorems have been applied.