In many control systems changes in the dynamics occur unexpectedly or are applied by a controller as needed. The time at which a controller implements changes is not necessarily known a priori. For example, many manufacturing systems and flight operations have complicated control systems, and changes in the control systems may be automatically implemented as needed in response to possibly unexpected external factors affecting the operations of the systems. Public policy makers in health-care have to launch timely and cost effective policies to deal with disease epidemics long term and short term. In drug dosing strategy for HIV treatment how treatment interruption strategies stimulate the body's own immune response and also control cost of treatment are important. Modeling of such systems lead to discontinuities in the dynamics governing the evolutions of the systems. We consider control problems governed by differential equations with discontinuities in the states at a sequence of points. The differential equations are referred to as impulsive differential equations, and the control problems as impulsive control problems. We consider general deterministic and nondeterministic impulsive control problems. Then, we consider the analysis of models coming from HIV treatment strategies, production planning, and asset allocation. The first chapter is devoted to a study of the qualitative analysis of an HIV treatment model. In Chapter two we present a mathematical model of an impulsive control problem. In Chapter three we consider the HIV treatment model considered in Chapter one along with HIV-immune system model. In Chapter four we consider a general impulsive stochastic control problem. In Chapter five we consider an example of production planning model. In the last chapter we study an asset allocation model. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com.bibliotheek.ehb.be/en-US/products/dissertations/individuals.shtml.]