Stability and optimal control for uncertain continuous-time singular systems

In this paper, problems of stability in measure and optimal control are considered for an uncertain continuous-time singular system which can be described by uncertain differential equations. Singular system is assumed to be regular and impulse-free. Under some given assumptions, the existence and uniqueness of the solution, and stability in measure of the singular system are presented. Then, by applying the principle of optimality and uncertainty theory, the equation of optimality for the optimal control model subject to the uncertain singular system is obtained. In the end of Sections 3-5, three examples are given to illustrate the results obtained.