Random Linear Systems Research Articles

Experimental study of a random linear system

Experimental study of a random linear system

On the moment stability of gaussian random linear systems

The theory of moment stability of random linear systems is extended to systems containing stationary, possibly correlated, Gaussian random parameters with rational nonwhite spectra. Sufficient conditions for the stability of the moments of the system are derived. Several stronger results are obtained for some restricted systems.

Analysis of linear distributed systems with random parameters and inputs

This paper is concerned with the statistical analysis of first-order linear distributed-parameter systems with random parameters and random inputs. In both cases, Gaussian processes are assumed. This work essentially extends the statistical theory available for analyzing random linear lumped-parameter systems to a restricted class of distributed-parameter systems.

Comments on “Moments of the Output of Linear Random Systems”

It is shown how the various moments of a random system can be obtained directly from the governing dynamical equations. An equation is given for the n-point probability distribution of dynamical systems.

Moments of the Output of Linear Random Systems

A method is presented for determining the differential equations of the output moments of a linear random system in which the coefficients are components of vector Markov processes. The method is based upon well-known results in applied stochastics. It appears considerably simpler than methods recently suggested for studying the behavior of linear random systems. A stability criterion previously published is obtained with little effort. Reasons are presented for disagreeing with published results that mean motion of linear random systems with Gaussian parameter variations is not influenced by these variations.

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.

On the mean square stability of random linear systems

The theory of random linear systems is extended to systems containing one or more non-independent parameters under the assumption that the parameter processes and the solution process have very widely separated spectra. It is shown that the second product moment of the solution satisfies a linear integral equation which can be solved in closed form in some important special cases. The mean square stability theory of equations containing one purely random coefficient initiated by Samuels .nd Eringen is developed further and extended to systems containing one narrow-band random parameter. Specific mean sjuare stability criteria are worked out for an RLC circuit with capacity variations that are a narrow-band stochastic function.

On the Mean Square Stability of Random Linear Systems

The theory of random linear systems is extended to systems containing one or more non-independent parameters under the assumption that the parameter processes and the solution process have very widely separated spectra. It is shown that the second product moment of the solution satisfies a linear integral equation which can be solved in closed form in some important special cases. The mean square stability theory of equations containing one purely random coefficient initiated by Samuels .nd Eringen is developed further and extended to systems containing one narrow-band random parameter. Specific mean sjuare stability criteria are worked out for an RLC circuit with capacity variations that are a narrow-band stochastic function.