A Corollary for Nonsmooth Systems

In this note, two generalized corollaries to the LaSalle-Yoshizawa Theorem are presented for nonautonomous systems described by nonlinear differential equations with discontinuous right-hand sides. Lyapunov-based analysis methods are developed using differential inclusions to achieve asymptotic convergence when the candidate Lyapunov derivative is upper bounded by a negative semi-definite function

On reduction of differential inclusions and Lyapunov stability

In this paper, locally Lipschitz, regular functions are utilized to identify and remove infeasible directions from set-valued maps that define differential inclusions. The resulting reduced set-valued map is point-wise smaller (in the sense of set containment) than the original set-valued map. The corresponding reduced differential inclusion, defined by the reduced set-valued map, is utilized to develop a generalized notion of a derivative for locally Lipschitz candidate Lyapunov functions in the direction(s) of a set-valued map. The developed generalized derivative yields less conservative statements of Lyapunov stability theorems, invariance theorems, invariance-like results, and Matrosov theorems for differential inclusions. Included illustrative examples demonstrate the utility of the developed theory

Formulation development and characterization of fast dissolving tablets of oxcarbazepine

The objective of this study was formulation development and evaluation of Oxcarbazepine Fast Dissolving Tablets (FDTs) prepared by sublimation technique where different sublimating agents like camphor and menthol were used with L-HPC and crospovidone as a superdisintegrants. Oxcarbazepine is an anticonvulsant drug used in the treatment of epilepsy and bipolar disorder. Each sublimating agent was used in concentration of 10-20 mg per tablet. Tablets were first prepared and then kept in hot air oven for sublimation. The prepared FDTs were evaluated for weight variation, thickness, drug content, friability, hardness, wetting time, water absorption ratio, in-vitro dispersion time, in-vitro disintegration time and in-vitro dissolution time. All formulations showed disintegration time ranging from 8 to 332sec. Optimized batch (SA6) was selected for the stability studies. The results of stability studies revealed that there was no remarkable difference in the tested parameters of promising formulation after storage for 3 months at 400 c ± 20 c 75% ± 5%RH and at room temperature 65% ± 5%RH as compared to initial results All the prepared formulae complied with Pharmacopoeia requirements of drug contents