Passivity Analysis Of Several Kind Of Switched Linear Systems

With the rapid development of science and technology in recent years,the passivity has attracted great interest as it is an effective tool for system analysis and solving practical industrial control problems.Switched system faces various problems in application due to its inherent characteristics.Then,this paper focuses on analyzing the performance of switched linear systems from the perspective of energy variation.It includes the exponential passivity of continuous switched systems and the passivity of interconnected switched systems.Due to the great progress in the technologies of computerized and networked control,the signal transmission in the control systems can cause problems such as time delays and packet losses.Therefore,this paper further considers the passivity of networked switched systems in the presence of continuous bounded packet losses.The main contents are summarized as follows:1.The passivity of continuous switched linear systems is studied.By analyzing every subsystem of the switched system,a “cycle” composed of active state and inactive state is indicated for each subsystem.Then based on the passivity of subsystem in its “cycle”,inequality conditions are designed to ensure the passivity of the whole switched system.When the subsystem is inactive,the loop-function technique is adopted to relax the requirements for the passive conditions.The criteria for exponential passivity and input/output exponential passivity of the switched system are established,and the obtained results are verified by a simulation.2.The passivity of feedback interconnected switched linear systems is investigated.The switching rule of one sub-switched systems is a Markov chain,and the other interconnected sub-switched systems switches according to the designed state-dependent switching law.The Markov switched system is regarded as a plant,while the state-dependent switched system serves as a dynamic controller.By exploiting the method that uses deterministic system to control the stochastic system,and analyzing the different combinations of the coupled two types of switching signals,sufficient conditions for the stochastic passive and the input/output stochastic passive of the interconnected switched system are finally provided.The proposed scheme allows the two sub-switched systems to switch at the same time or different time,and the number of subsystems in their internals can also be different.The results are validated by a simulation.3.The passivity of the networked switched linear system with bounded packet losses is further considered.Firstly,the passive conditions for the discrete switched system under the ideal transmission are analyzed and presented.Based on this result,we mainly see inside the influences on the passive,which are raised by arbitrary packet losses and Markovian packet losses.For different types of packet losses,the switch within the packet-loss process is considered.Then by analyzing the interplay between the switches and packet losses,the passivity under arbitrary packet losses and the stochastic passivity under Markovian packet losses are established based on the maximum packet losses.A simulation example is applied to illustrate the obtained results.