Sharif Digital Repository

Eigenvalue analysis is a fundamental tool in control issues, however, in some abnormal matrixes it can lead to an incorrect judgment of the matrix dynamic behavior. Pesudospectra, as an eigenvalue generalization, can provide more extensive information of the system dynamic behavior, whereas, the obtained data from eigenvalue analysis can be incomplete. In applying robust controllers, the concept of uncertainty has been attracted researcher interest in system modelling, nevertheless, the controller implementation may not be fault free or the parameters may vary over time. In this project the aforementioned issue will be studied and additionally, the pseudospectra will be employed to design a... 

The present thesis introduces a new method to design non-fragile controllers. The idea of design is to set the centroid of the stability region as the tuning point of two-parameter controllers. This ideahas been motivated by the fact that the centroid of a convex region belongs to a set of pointsthat have farthest distance from its boundary. In case that stability region is not convex, a correction may be needed because the centroid of non-convex region may be very near to or out of its boundary. One modified version of design method when stability region is not convex, is to find maximum convex sub-area inside stability region and set its centroid as the tuning point of controller... 

Most of the robust or optimal controllers can produce extremely fragile controllers [1], in the sense that vanishingly small perturbations of the coefficients of the designed controller destabilize the closed-loop control system. Modern control methods, including robust control, lead to high order controllers.Often times a reduced order controller is implemented. As a result, need for low order control design reducing controller’s ensitivity is tangible. Based on studies carried out, properties of normal matrices can be employed to define a fragility measure. In this thesis, a new convex criterion measuring controller fragility is defined. Then, a more resilient reduced order controller can... 

One of the issues in the design and synthesis of the state or output feedback controller is the issue of fragility as the existence of disturbance in the coefficients of the designed controller causes instability in the controlled closed-loop system or leads to deterioration of its performance. The need to consider this point results in some novel approaches for designing the non-fragile controllers. Accordingly, defining criteria for measuring fragility is crucial.As well, due to the considered practical problems in the implementation of ordinary designed robust and optimal controllers, non-reachability of all the states of dynamical systems, and the boundedness for the quantity of the...