Stability of linear second-order equations with time-varying coefficients.
Sufficient conditions for asymptotic stability of linear second order equations with time varying coefficients
Walker, J. A.↗
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The stabilization of a nonlinear system using a linear system estimator
Nonlinear systems stabilization with linear system estimator output state to provide feedback for asymptotic stability of overall system
Strane, R. E.↗
Passivity/Lyapunov based controller design for trajectory tracking of flexible joint manipulators
A passivity and Lyapunov based approach for the control design for the trajectory tracking problem of flexible joint robots is presented. The basic structure of the proposed controller is the sum of a model-based feedforward and a model-independent feedback. Feedforward selection and solution is analyzed for a general model for flexible joints, and for more specific and practical model structures. Passivity theory is used to design a motor state-based controller in order to input-output stabilize the error system formed by the feedforward. Observability conditions for asymptotic stability are stated and verified. In order to accommodate for modeling uncertainties and to allow for the implementation of a simplified feedforward compensation, the stability of the system is analyzed in presence of approximations in the feedforward by using a Lyapunov based robustness analysis. It is shown that under certain conditions, e.g., the desired trajectory is varying slowly enough, stability is maintained for various approximations of a canonical feedforward.
Sicard, Pierre↗
Application of Model Reference Adaptive Control System to Instrument Pointing System /IPS/
A Model Reference Adaptive Controller (MRAC) is derived for a Shuttle payload called the Instrument Pointing System (IPS). The unique features of this MRAC design are that total state feedback is not required, that the internal structure of the model is independent of the internal structure of the IPS, and that the model input is of bounded variation and not required a priori. An application of Liapunov's stability theorems is used to synthesize a control signal which assures MRAC asymptotic stability. Exponential observers are used to obtain the necessary state information to implement the control synthesis. Results are presented which show how effectively the MRAC can maneuver the IPS.
Waites, H. B.↗
Supporting research studies to booster flight control problems Final report
Asymptotic stability and response of nonlinear systems
ASYMPTOTIC FUNCTION↗
Stability analysis of relay-control systems via the direct method of lyapunov
Computational technique for constructing Liapunov functions for estimating domain of asymptotic stability of nonlinear control systems
NONLINEAR SYSTEM↗
Stability regions of large-scale systems.
Using an aggregated comparison system, methods are developed for estimating regions of asymptotic stability for large-scale systems composed of interconnected, exponentially stable subsystems; in general some of these subsystems are not globally stable. Three different forms of Liapunov functions are shown to be suitable for describing the stability behavior of the aggregated system, but one form in particular (heretofore not used in this context) is found to be the most natural. Using this function, some general results are obtained.
Weissenberger, S.↗
Stability regions of large-scale systems
Using an aggregated comparison system, methods are developed for estimating regions of asymptotic stability for large-scale systems composed of interconnected, exponentially stable subsystems; in general, some of these subsystems are not globally stable. Three different forms of Liapunov functions are shown to be suitable for describing the stability behavior of the aggregated system, but one form in particular, heretofore not used in this context, is found to be the most natural. Using this function, some general results are obtained.
Weissenberger, S.↗
Two counterexamples to Aizerman's conjecture.
Oscillation formation by violation of sufficient conditions of asymptotic stability in linear system
STABILITY TEST↗
Design implementation in model-reference adaptive systems
The derivation of an approximate error characteristic equation describing the transient system error response is given, along with a procedure for selecting adaptive gain parameters so as to relate to the transient error response. A detailed example of the application and implementation of these methods for a space shuttle type vehicle is included. An extension of the characteristic equation technique is used to provide an estimate of the magnitude of the maximum system error and an estimate of the time of occurrence of this maximum after a plant parameter disturbance. Techniques for relaxing certain stability requirements and the conditions under which this can be done and still guarantee asymptotic stability of the system error are discussed. Such conditions are possible because the Lyapunov methods used in the stability derivation allow for overconstraining a problem in the process of insuring stability.
Boland, J. S., III↗
Absolute stability of a system of nonlinear networks interconnected by lossless transition lines
Nonlinear networks interconnected by lossless transmission lines, deriving global asymptotic stability condition
De Figueiredo, R. J. P.↗
A controller design for multi-body large angle maneuvers
Active large angle slewing maneuvers of a multi-body flexible dynamic system are investigated. An appropriate state variable transformation and a feedback linearization technique are employed to transform the dynamics of the nonlinear system to a new state that is more amenable to control design procedures. Closed-loop feedback algorithms are implemented to perform slewing maneuvers, while simultaneously suppressing flexural vibrations of the system. Stability of this class of nonlinear systems is also investigated, whereby a sufficient condition for asymptotic stability of the system is established. Numerical examples are presented to demonstrate the proposed active control algorithms.
Ghaemmaghami, Peiman↗
On a system of equations in automatic control theory.
Asymptotic stability of automatic control equations for nonsingular and singular cases, establishing existence conditions for Liapunov function
AUTOMATIC CONTROL↗
On the stability, storage capacity, and design of nonlinear continuous neural networks
The stability, capacity, and design of a nonlinear continuous neural network are analyzed. Sufficient conditions for existence and asymptotic stability of the network's equilibria are reduced to a set of piecewise-linear inequality relations that can be solved by a feedforward binary network, or by methods such as Fourier elimination. The stability and capacity of the network is characterized by the post synaptic firing rate function. An N-neuron network with sigmoidal firing function is shown to have up to 3N equilibrium points. This offers a higher capacity than the (0.1-0.2)N obtained in the binary Hopfield network. Moreover, it is shown that by a proper selection of the postsynaptic firing rate function, one can significantly extend the capacity storage of the network.
Guez, Allon↗
Optimal filtering and filter stability of linear stochastic delay systems
Optimal filtering equations are obtained for very general linear stochastic delay systems. Stability of the optimal filter is studied in the case where there are no delays in the observations. Using the duality between linear filtering and control, asymptotic stability of the optimal filter is proved. Finally, the cascade of the optimal filter and the deterministic optimal quadratic control system is shown to be asymptotically stable as well.
Kwong, R. H.-S.↗
Estimation and filter stability of stochastic delay systems
Linear and nonlinear filtering for stochastic delay systems are studied. A representation theorem for conditional moment functionals is obtained, which, in turn, is used to derive stochastic differential equations describing the optimal linear or nonlinear filter. A complete characterization of the optimal filter is given for linear systems with Gaussian noise. Stability of the optimal filter is studied in the case where there are no delays in the observations. Using the duality between linear filtering and control, asymptotic stability of the optimal filter is proved. Finally, the cascade of the optimal filter and the deterministic optimal quadratic control system is shown to be asymptotically stable as well.
Kwong, R. H.↗
Invariance and stability for bounded uncertain systems.
The positive limit sets of the solutions of a contingent differential equation are shown to possess an invariance property. In this connection the 'invariance principle' in the theory of Lyapunov stability is extended to systems with unknown, bounded, time-varying parameters, and thus to a large and important class of nonautonomous systems. Asymptotic stability criteria are obtained and applied to guaranteed cost control problems.
Peng, T. K. C.↗
Fokker-Planck response of stochastic satellites
The present investigation is concerned with the effects of stochastic geometry and random environmental torques on the pointing accuracy of spinning and three-axis stabilized satellites. The study of pointing accuracies requires a knowledge of the rates of error growth over and above any criteria for the asymptotic stability of the satellites. For this reason the investigation is oriented toward the determination of the statistical properties of the responses of the satellites. The geometries of the satellites are considered stochastic so as to have a phenomenological model of the motions of the flexible structural elements of the satellites. A widely used method of solving stochastic equations is the Fokker-Planck approach where the equations are assumed to define a Markoff process and the transition probability densities of the responses are computed directly as a function of time. The Fokker-Planck formulation is used to analyze the response vector of a rigid satellite.
Huang, T. C.↗