Differential Equations and Control Theory

Research Topic - Differential Equations and Control Theory

The concept of stability in a common and engineering sense reflects the necessity to keep response of a disturbed system within accepted limits. If deviations describing response of the system from a given regime (e.g. state of equilibrium) lie within prescribed limits, the system is called stable. Otherwise, the system is called unstable. Disturbances, response and prescribed limits can be specified in each case in different ways. Robustness is an approach to feature persistence in systems for which we do not have the mathematical tools to use the approaches of stability theory. The problem could in some cases be reformulated as one of stability theory, but only in a formal sense that would bring little in the way of new insight or control methodologies. The robust stability problem considers the stability problem of systems that contain some uncertainties. As is well known, it is usually impossible to describe a practical system exactly. First, there are often parameters or parasitic process that are not complete. Second, due to the limitation of mathematical tools available, we usually try to use a relatively simple model to approximate a practical system. As a result, some aspects of the system dynamics (known as unmodeled dynamics) are ignored. Third, some control systems are required to operate within a range of different operating conditions. To capture these uncertain factors, it is often possible to identify a bounding set such that all the possible uncertainties fall within this set and yet it is not too difficult to analyze mathematically.

Department & Campus

Department of Mathematics, Coimbatore

Skillsets Preferred from Applicants

CSIR-UGC- NET or Good in B.Sc., and M.Sc., Mathematics score