A model for cage formation in colloidal suspension of laponite

In this paper we investigate glass transition in aqueous suspension of synthetic hectorite clay, laponite. We believe that upon dispersing laponite clay in water, system comprises of clusters (agglomerates) of laponite dispersed in the same. Subsequent osmotic swelling of these clusters leads to increase in their volume fraction. We propose that this phenomenon is responsible for slowing down of the overall dynamics of the system. As clusters fill up the space, system undergoes glass transition. Along with the mode coupling theory, proposed mechanism rightly captures various characteristic features of the system in the ergodic regime as it approaches glass transition.Comment: 12 pages, 1 figures. The Journal of Chemical Physics, in pres

Optimal output feedback control of linear systems in presence of forcing and measurement noise

The problem of obtaining an optimal control law, which is constrained to be a linear feedback of the available measurements, for both continuous and discrete time linear systems subjected to additive white process noise and measurement noise was Necessary conditions are obtained for minimizing a quadratic performance function for both finite and infinite terminal time cases. The feedback gains are constrained to be time invariant for the infinite terminal time cases. For all the cases considered, algorithms are derived for generating sequences of feedback gain matrices which successively improve the performance function. A continuous time numerical example is included for the purpose of demonstration

Regions of attraction and ultimate boundedness for linear quadratic regulators with nonlinearities

The closed-loop stability of multivariable linear time-invariant systems controlled by optimal linear quadratic (LQ) regulators is investigated for the case when the feedback loops have nonlinearities N(sigma) that violate the standard stability condition, sigma N(sigma) or = 0.5 sigma(2). The violations of the condition are assumed to occur either (1) for values of sigma away from the origin (sigma = 0) or (2) for values of sigma in a neighborhood of the origin. It is proved that there exists a region of attraction for case (1) and a region of ultimate boundedness for case (2), and estimates are obtained for these regions. The results provide methods for selecting the performance function parameters to design LQ regulators with better tolerance to nonlinearities. The results are demonstrated by application to the problem of attitude and vibration control of a large, flexible space antenna in the presence of actuator nonlinearities