Non-fragile Guaranteed Cost Control For Uncertain Descriptor Systems

Many practical processes can be modeled as descriptor systems, such as constrained control problems, electrical circuits, certain population growth models and singular perturbations. In the past several decades, stability and control problems of descriptor systems have been extensively studied due to the fact that the descriptor system better describes physical systems than the state-space systems. Compared with state-space systems, the descriptor system has a more complicated yet richer structure. Considering the effect of time delay and uncertainty on the dynamical performance of the systems, robust stability and control problems have been more recently investigated for the uncertain descriptor systems with time delay. However, most results are under the assumption that the designed controller can be exactly implemented. When the controller can't be exactly implemented, we should design non-fragile controller for uncertain descriptor systems, this is the main content of this paper, specifically as follows:In chapter 3, we consider the design problem of non-fragile guaranteed cost controller for uncertain descriptor systems with time delays. The considered uncertainties are norm-bounded and the time delays are time-varying and exist both in the state and control input. The designed controller with inaccuracies exist in control gain can guarantee the closed-loop system is regular, impulse-free, exponentially stable and there is an upper bound of the cost function.In chapter 4, the problem of non-fragile H-infinity control for uncertain descriptor systems with time-varying delays is addressed. The controller is designed when parameter uncertainties exist in system matrix, delayed system state matrix, control input matrix, delayed control input matrix, and inaccuracies exist in control gain, so as to guarantee that the closed-loop system is regular, impulse-free,α?stable ,also satisfies a prescribed H-infinity performance condition.In chapter 5, we generalize the concepts of finite time bounded to linear singular systems. Then, non-fragile finite time control problem is considered for linear singular systems with parametric uncertainties and exogenous disturbance,the controller can guarantee that the closed-loop system is impulse-free and finite time bounded.