EFFECT OF STATIC STRETCHING OF HAMSTRING ON NON-SPECIFIC LOW BACK PAIN

Objective: To determine the effect of static stretching of hamstring muscle on the non-specific low back pain. Methodology: A Quasi-Experimental study was conducted in Rabia Moon Institute of Neurology which total 30 participants were included through non-probability purposive sampling. Thirty participants were selected who fulfilled our inclusion criteria, they were divided into two groups; group A or treatment group received conventional physiotherapy treatment as well a static stretching exercise protocol for 5 days. Group B or control group received conventional physiotherapy treatment only. VAS (Visual analog scale) and Oswestry Disability questionnaire, SFGD (Standing Finger to ground Distance,) PSLR (passive straight leg raise) for both legs were measured pre- and post-treatment. Result: A total of 30 patients aged 20-55 were included in the study. Mean age of the participants was found to be 37.88 years.  The difference in means of all the assessment parameters pre and post-treatment for both groups were analyzed through paired t-test. There was a significant improvement in VAS, SFGD, Passive Straight leg Raise PSLR (right leg), PSLR (left leg) and level of disability pre- and post-treatment in the treatment group. Conclusion: This present study concluded that static stretching of hamstrings is effective in decreasing non-specific low back pain.

Robust Osberver Synthesis for Lipschitz and One-Sided Lipschitz Nonlinear Systems

Practically, system dynamics are nonlinear, requiring the estimation of unknown states, which encourages the observer schemes to be implanted in control structures. This dissertation presents estimation andltering of the Lipschitz and one-sided Lipschitz nonlinear systems and provides robustness against L2 normbounded disturbances and parameter uncertainties for state estimation. The developed approaches overcome the practical consequences of time-delays, perturbations and disturbances. Robust state estimation for Lipschitz and one-sided Lipschitz nonlinear systems is established by the adoption of Luenberger-like observer scheme, which is extended to the generalizedltering scheme to exhibit diverging manifolds, namely, the conventional static-gainlter and dynamiclter as speci c scenarios. Further, the presented estimation schemes unfolded the application based designs, including observer-based control of the nonlinear systems. Observer-based controller application is a duple process: It requires the estimation of unknown states atrst step, while in second stage, a controller is designed using these estimated states. A decoupling condition, necessary and su cient, for the presented approach, is explored to obtain controller and observer gains. Moreover, the controller scheme is further extended to overcome time-varying parametric uncertainties and norm-bounded disturbances. Convex optimization is adopted to solve the nonlinear constraints by combining nested bilinear-term-solver approach with a nonlinear optimization-based cone complimentary linearization. Comprehending the contributions of this dissertation, robust estimation based approaches for Lipschitz and one-sided Lipschitz systems are explored under output delays. Delay-range-dependent stability criterion is adopted to establish the stability, which foregrounds less conservative schemes. Robust generalizedltering for delayed nonlinear systems extends the concept of estimation tolter the noises and perturbations. Furthermore, robust estimation scheme for the nonlinear systems against parametric uncertainties is provided under measurement delay. Robust observer-based controller schemes as applications of the proposed estimation methods are studied. Numerical simulation results of practical systems are provided.