Stability Of Random Systems Research Articles

Parametric Oscillations in Elastic Systems Excited by Random Perturbations with a Finite Correlation Radius

The paper addresses the dynamic stability of random systems. The dynamic stability bounds are established on the basis of the definition of stability with respect to moment functions. The differential equations for these functions are derived by approximating an exponentially correlated normal random process by a random process with a finite number of states. These results are shown to agree with the well-known results for parametric white noise excitation

Competitive processes II. Stability of random systems

In this work, by employing the concept of vector Lyapunov functions and the theory of random differential inequalities, the stability analysis of random competitive systems is initiated in a systematic and unified way. Furthermore, an attempt has been made to formulate and partially resolve the “deterministic vs. stochastic”, and the “complexity vs. stability” problems in stochastic competitive processes. Finally, the usefulness of the stability analysis of the competitive systems has been demonstrated by exhibiting several well-known examples of competitive processes in biological, medical, physical and social sciences in a coherent way.

On the stability of a class of non-stationary non-linear random systems

The stability of the trivial equilibrium solution of a class of non-linear differential equations with a non-stationary absolutely integrable random coefficient is studied. The mean square stability of random systems is discussed and stability theorems of Bertram and Sarachik (1959) are stated. It is shown that the equilibrium null solution is mean square stable under some mild conditions. Some examples are also considered.

Comments on “On the Stability of Random Systems”

Dr. Samuels [1] is to be congratulated on a most interesting paper. It is unfortunate that a number of errors appear in Sec. III which invalidate both that section and Sect. IV.

Remarks on Dr. Caughey's Comments on My Paper entitled “On the Stability of Random Systems, Etc.”

Remarks on Dr. Caughey's Comments on My Paper entitled “On the Stability of Random Systems, Etc.”

On the Stability of Random Systems and the Stabilization of Deterministic Systems with Random Noise

A general theory of mean square stability of random linear systems is developed when several system parameters vary as white noise stochastic processes. It is found that stability in mean square is determined from the character of the roots of a determinantal equation involving the Fourier transforms of double products of the weighting functions of the “average” system and the spectral densities of the parameter processes. The general theory is applied to the mean square stability of an RLC circuit in which the resistance and capacitance have purely random fluctuations. In the course of the study, a new type of dynamic stability is predicted, namely, the possibility of stabilizing unstable deterministic systems with random noise. Preliminary experimental studies appear to confirm this theoretical prediction.