## Control TheoryControl Theory has contributed in a very fundamental way to technological progress in many areas, in recent decades. It has even had a large impact on areas such as biological modeling and economics. The classical theory (automatic control systems) has been widely used in modern society, it ranges from simple application such as in the temperature control to highly sophisticated systems such as airplanes and satellites. It is notewoth, as a landmark of technological application, that control theory has played a fundamental role in the success of the Apollo project, in the development of the F-16 jets, and more recently in the continued success of the American space airbus and others space programs. A research project on uncertain dynamical system control: methods, algorithms and applications is being developed by Marcelo D. Fragoso, C. E. Souza, O. Costa, J. Geromel, J. B. do Val. This research deals with the problem of establishing criteria for stability, to develop relevant control and filtering strategies for uncertain dynamical systems. The project contemplate also algorithm implementation and applications. Besides the usual additive disturbances, and parametric uncertainties, in this research project we shall be particularly interested in the class of dynamical systems which are subjected to uncertainty (change) in their structures as a consequence of abrupt phenomena. These uncertainties are characterized in the model via a Markov chain(continuous or discrete). These systems are also known in the literature as Markovian Jumping Systems(MJS) and constitute an important class of hybrid systems. The MJS are seen by many researchers as a real alternative for reaching failure tolerance behaviour in control systems, and consequently highly relevant for control theory (belongs to what is known in the specialized literature as safety-critical and high-integrity systems. Although many methodologies have been developed in recent years in the theory of control, the approaches known as Stochastic Control and Robust Control are certainly those which are more promising and which outstand in the treatment of uncertain dynamical systems control problems, and are the approaches of main interest in this project. |