Singular System Analysis And Synthesis Methods And Its Application In Structural Systems

Singular system, which is more suitable to describe a lot of practical systems than the regular system, has been widely used to describe many practical systems, such as, power grid system, singularly perturbed systems, leontief economic model, chemical process, nuclear reactor system, and so on. Singular system contains not only the slow subsystem which is described by differential equations (for continuous singular system) or difference equations (for discrete singular system), but also the fast subsystem which is described by algebraic equations. Thus, the stability analysis and stabilizing controller design for singular system are much more complicated than those for regular system. The analysis of singular system requires the consideration of not only stability, but also regularity and the absence of impulses (for continuous singular system) or causality (for discrete singular system) simultaneously. In addition, due to the information transmission and data processing, etc., time delay often exists in the physical systems. During the analysis and synthesis of the actual systems, inappropriate handling of time delay often causes performance deterioration, or even leads to instability. For singular system, time-delay may even damage the regularity, causality or the absence of impulses of the system. Therefore, how to obtain the stability analysis and controller synthesis results (especially delay-dependent results) for the time-delay singular system is of very important practical significance.Aiming at the problems about time delay and uncertainty in singular system, the delay-dependent sufficient conditions for the stability and stabilization of constant and time-varying delay singular systems are developed in this paper. Furthermore, the obtained results for singular systems are extended to the stability analysis for structural systems, and the passive control and active control methods for structure system are discussed in this paper.The work of this paper mainly contains three parts:(1) By appropriate choice of the Lyapunov function, the delay-dependent sufficient conditions for admissibility, robust admissibility, stabilizability, and robust stabilizability of continuous and discrete singular systems are studied based on integral inequality and free weight matrix methods. The main contribution of this section is the introduction of a new Lyapunov function, namely, partial non-positive (PNP) Lyapunov function, by which the less conservative results about system analysis and synthesis are obtained.(2) Aiming at the time-varying delay singular system, the delay-dependent sufficient conditions for admissibility, robust admissibility, stabilizability, and robust stabilizability of continuous singular system and discrete lime-varying delay Markovian jump singular system are studied by using model transformation and delay-partitioning technique. Numerical examples are provided to demonstrate the effectiveness of the proposed methods.(3) The description form of singular system is extended to describe structural system. When the parameter-uncertainties appear in the structural systems, singular description form can avoid the coupling of the uncertain parameters and reduce the conservatism of the system model. In the passive control of structural system, the global optimal TMD parameters design method is obtained by introducing the optimization of genetic algorithm. In the active control of structural system, the parameter-dependent controller design method is presented for structural system driven by electro-hydraulic servo system, and its effectiveness is illustrated by numerical simulation.