Modeling And Analysis For Switched Linear Systems

Switched linear systems (SLSs) are a class of special hybrid systems, which is characteristic of continuity as well as discreteness. On the one hand, in real life and engineering application, many practical system models are composed of switched linear systems. On the other hand, compared with linear analysis method, under certain conditions, nonlinear systems can be analyzed by approximately modeling them as switched linear systems so that the accuracy of the solution is increased. In addition, system performance can be improved by switching characteristics of switched linear systems. In this paper, on the base of previous study in SLSs, periodic orbits modeling and stability analysis etc in SLSs are studied systematically. The main research contents are as follows(1) Frequency domain modeling and analysis method for periodic orbit in SLSs are studied systematically. The meaning of describing function method, time variable transfer function method and Volterra series method and their application in SLSs are illustrated. Volterra series frequency domain model of a class SLSs is build, and its harmonic characteristics are analyzed.(2) Average modeling methods for periodic orbit in different types of SLSs are studied systematically. Sliding-mode variable structure average model of free-running current-programmed (?)uk converter is proposed. Bifurcation characteristics of equilibrium points are analyzed. Conditions for the occurrence of various bifurcations and parameter space of stability operation are derived analytically. The continuous time small signal average model of charge pump phase locked loops (CPPLL) is given. A blocking design method for high order loop filter of CPPLL is proposed. By this method, desired bandwidth as well as optional high order and type of CPPLL can be derived. By analyzing stability and characteristics of CPPLL, the chosen scope of the loop parameters can be determined and the conclusion that n order n type of CPPLL is superior to others is derived.(3) Time domain modeling method and stability for periodic orbits of non-autonomous, non-periodic switching switched linear systems are studied. The discrete-time mapping model for non-autonomous switched linear systems is derived. The coordinates of the switched points of the periodic orbit on each switching surface and the Jacobian matrixes at corresponding fixed point are obtained. The stability of fixed point is analyzed. Theoretical analysis and simulation results for the switched linear Duffing oscillator and Colpitts oscillator are presented to illustrate the proposed method.(4) Discrete time mapping model and method of stability analysis for periodic orbits with a segment of sliding orbit in switched linear systems are studied. Sliding mapping and impact mapping are obtained by solving respective differential equation. A generalized discrete time mapping model for a cycle is derived according to three scenarios: cross-sliding, multi-sliding, and grazing sliding. The Jacobian matrixes at corresponding fixed-point are obtained. The stability of the periodic orbit is analyzed. Theoretical analysis and simulation results for a third order relay feedback system and a second order autonomous oscillating circuit are presented to illustrate and confirm the proposed model and method.(5) Nonlinear bifurcation behaviors in input-series output-parallel (ISOP) DC-DC converters under peak current mode in continuous conduction mode are investigated. Circuit simulation demonstrates typical nonlinear phenomena occurring in the ISOP DC-DC converters. A precise stroboscopic mapping mode integrated with Filippov method is presented to analyze the stability and instability bifurcation phenomena in the ISOP DC-DC converters. Stable parameters scope and bifurcation boundary line are determined.