In existing dynamic mode operation of Atomic Force Microscopes (AFMs) steady-state signals like amplitude and phase are used for detection and imaging of material. Due to the high quality factor of the cantilever probe the corresponding methods are inherently slow. In this dissertation, a novel methodology for fast interrogation of material that exploits the transient part of the cantilever motion is developed. This method effectively addresses the perceived fundamental limitation on bandwidth due to high quality factors. It is particularly suited for the detection of small time scale tip-sample interactions. Analysis and experiments show that the method results in significant increase in bandwidth and resolution as compared to the steady-state-based methods;In atomic force microscopy, bandwidth or resolution can be affected by active quality factor (Q) control. However, in existing methods the trade off between resolution and bandwidth remains inherent. Observer based Q control method provides greater flexibility in managing the tradeoff between resolution and bandwidth during imaging. It also facilitates theoretical analysis lacking in existing methods;In this dissertation we develop a method for exact constructive controllability of quantum-mechanical systems. The method has three steps, first a path from the initial state to the final state is determined and intermediate points chosen such that any two consecutive points are close, next small sinusoidal control signals are used to drive the system between the points, and finally quantum measurement technique is used to exactly achieve the desired state. The methodology is demonstrated for the control of spin-half particles in a Stern-Gerlach setting;In this dissertation, a novel closed-loop real-time scheduling algorithm is developed based on dynamic estimation of execution time of tasks based on both deadline miss ratio and task rejection ratio in the system. This approach is highly preferable for firm/soft real-time systems since it provides a firm performance guarantee in terms of high guarantee ratio. Proportional-integral controller and H-infinity controller are designed for closed loop scheduling. Simulation studies showed that closed-loop dynamic scheduling offers a better performance over the openloop scheduling under all the practical conditions.