Study Of Robust Control, Filtering And Model Reduction For Time-Delayed Linear Parameter-Varying Systems

Linear parameter-varying (LPV) system is an important class of time-varying systems and its state space matrices are time-varying parameters matrices which can be measured in real time and vary in a compact set. In recent year, theoretical research for the LPV system has been concerned from scholars at home and abroad because it describe the characters of nonlinear and time-varying of dynamic systems. At the same time in nature, the systems are often disturbed from external persistent bounded signals. Therefore, the study of L1 performance criterion that is measure by signal peak value and minimizes the worst case peak-to-peak gain has important significations. In addition, time-delay often exists in actual physical systems, which often result in instability and performance degradation of systems. Consequently, the study of time-delay LPV system has important theory and practical significance.This thesis first proposes and proves L1 performance criterion for time-delay LPV systems and it may extend to LPV systems without delay and with multiple-delays. The emphasis is focus on time-delay dependent robust L1 filtering, L1 control and L1 model reduction for LPV systemsApplying parameter-dependent Lyapunov functional approach and parameter linear matrix inequality (PLMI) technology,we propose and prove that delay dependent L1 performance criterion of time-delay LPV systems that gurantees the system to be asymptotically stable and have the worst case peak-to-peak performance constraint. There exists the coupling between the parameter-dependent Lyapunov matrices and the system matrices in the above L1 performance criterion. Introducing a slack matrix and applying Projection Lemma, we can obtain decoupled L1 performance. L1 performance is extended to LPV system without delay and with multiple-delays. We give the sufficient conditions for the existence of system that is asymptotically stable and satisfies L1 performance respectively.First of all, According to decoupled L1 performance criterion, we get the sufficient conditions for the existence of an admissible L1 filter. By approximating the function space with finite basis functions and gridding technology, Infinite dimensional PLMI are transformed into finite dimensional PLMI and further into feasible problems subject to a group of PLMI constraints.Secondly, adopting the gain scheduling technology, we design the state feedback controller and output feedback controller. But there is the form of inverse constraints of PLMI in output feedback controller. Because the obtained sufficient conditions are not described in the form of PLMI, the cone complementary linearization (CCL) method is used to cast them into minimization problems subject to PLMI constraints. Thus, we can solve the parameters of controller using standard mathematical software.Finally, according to convex linear method and variable substitution approach, design method of L1 reduced-order systerm is given and is transformed into convex optimization problem. A numerical example is provided to illustrate the effectiveness of the proposed design method.