| Switched systems are distinctive subclass of hybrid systems composed of a family of continuous-time or discrete-time subsystems with a criterion that rules the switching among them. Since many physical processes possess switched nature, and many real-world applications resort to switching strategy to improve the control performance, switched systems have received a great attention during the recent decades. Due to the different natures of subsystems and switching rules, switched systems can be divided into different types, and accordingly the stability analysis methods should also be special and targeted. On the other hand, most of the existing researches about switched systems focus on the asymptotic stability, i.e. the steady-state performance at infinite time interval. However in many practical applications, the values of states are not allowed to exceed a certain bound during a fixed time interval, e.g. to avoid saturation or excitation. Therefore, the theories of finite-time stability (FTS) and finite-time boundedness (FTB), which focus on the transient response of dynamical systems over a finite time interval, are of important significance. Similar to non-switched systems, switched systems can be divided into linear switched systems, nonlinear switched systems and generalized switched systems. Based on the existing researches about switched systems, this paper proposes the FTS (FTB) analysis methods for fuzzy switched systems, large-scale switched systems and affine switched systems, where fuzzy switched systems represent nonlinear switched systems, large-scale switched systems represent generalized switched systems and affine switched systems represent linear switched systems. Then the results of switched systems are applied in the modeling and stability analysis of three-phase sinusoidal pulse width (SPWM) inverter and active power filter (APF).Firstly, time-dependent methods are utilized to design the finite-time stabilizing controller and H∞ controllers for fuzzy switched systems and large-scale switched systems. For fuzzy switched systems, parallel distributed compensation (PDC) scheme is employed to design state feedback controllers and output feedback controllers respectively under the situation that the whole state is observable and the full state is not observable, in order to stabilize the FTS/FTB of the whole system. For large-scale switched systems, in which there are different switching laws and state variables of subsystems, and subsystems are interconnected, this paper proposes a set of decentralized finite-time stability(DFTS) and decentralized finite-time boundedness(DFTB) analysis methods based on the concept "decentralized", and the finite-time H∞ controllers are designed to ensure the whole system DFTS or DFTB.For time-dependent affine switched systems, we disscuss the FTB analysis and stabilization problems, and compare the conservativeness of FTB condtions under different switching law knowledges. The results demonstrate that the more knowledges of switching laws we know, the less conservative FTB conditions we obtain. Due to the existence of affine terms, the asymptotic stability of affine switched system can not be ensured under the time-dependent switching signals. Therefore, it is of both theoretical and practical significance to analysis the FTB of affine switched systems by average dwell time design.Because of power switching devices, power electronic circuit is a typical switching system. In order to avoid the defects brought by traditional methods for modeling and analysis of power electronic circuit, this paper proposes a novel modeling and analysis method based on switched system theory. In this paper, we take three-phase SPWM inverter and active power filter(APF) for example, which are time-dependent and state-dependent switching systems respectively. SPWM inverter can be regared as a typical periodic afFine switched system. When the affine term is zero, we can analyze its asymptotic stability via the stability equivalence between periodic switched system and polytopic model. When the affine term is not zero, asymptotic stability of the periodic affine switched model for SPWM inverter can not be guaranteed, and we focus on the FTS/FTB analysis in this situation. For periodic switched systems, the subsystems and the switching process are just the same in any period, so that the FTB conditions in any switching period interval can guarantee the stability of the whole system when t tâ†'∞. On the other hand, for three-phase APF device, the switchings are determined by the value of error state, and APF can be regared as an state-dependent affine switched system. Based on affine switched system theory, this paper discusses the modeling and stability analysis of APF under the given switching laws, i.e. the given harmonic current tracking algorithms. Considering the time-delay phenomenon of APF device, the H∞ controllers are designed to reduce the influence of time-delay on the system stability and ensure the harmonic current compensation performance of APF. |
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