Analysis Of QSR-Dissipativity And Control Design For Switched Nonlinear Systems

Dissipativity of dynamical systems describes an energy evolution law of systems in terms of input and output<which means that the stored energy in a system is no more than the supplied energy from outside the system.In view of this,dis-sipativity plays an important role in the research of nonlinear systems,and is a powerful tool in analysis and design of nonlinear systems.For switched systems,in addition to the energy evolution of each subsystem,energy transfer and exchange exist between subsystems.The energy evolutions determine the dynamic behavior of switched systems to an appreciable extent.Therefore,energy and energy-based control are more important for switched systems.However,the traditional dissipa-tive concept is not only too strict,but also difficult to describe the energy exchange between subsystems.Finding out a suitable research tool is a key to the dissipa-tive development of switched systems.The multiple storage functions overcome the limitations of all subsystems sharing a storage function and become a main method of studying the dissipativity of switched systems.However,on the one hand,most of the existing works require non-increasing of the multiple storage functions both on switching instants and at active time intervals,which brings a certain conser-vatism to the dissipativity.Although the two conditions have been improved later,the verifiability of conditions can not be guaranteed.On the other hand,it is still a challenge to construct multiple storage functions of switched nonlinear systems.To a certain extent,it blocks the development of dissipative theory of switched sys-tems.At present,the research on the dissipativity of switched nonlinear systems is far from mature.QSR-dissipativity,which takes the supply rate as a relatively simple quadric form of an input and an output,is a typical type of dissipativity and facilitates the performance analysis and control design of systems.Particularly,as two special cases of QSR-dissipativity,passivity and L₂/l₂-gain are important for stability analysis of systems,and play a crucial role in the study of switched nonlinear systems.QSR-dissipativity,passivity,finite-time passivity and L₂/l₂-gain of switched nonlinear systems are studied in this dissertation.On the basis of QSR-dissipativity analysis,feedback passification and H_? control problems are addressed.Taking the property of passive systems into account,we also investigate passivity-based stabilization of switched nonlinear systems.The main theoretical results are as follows:?.Local strict QSR-dissipativity of a switched nonlinear system is studied using the linearization technique.First,we design a switching law to make a switched nonlinear system locally strictly QSR-dissipative even if each subsystem is not lo-cally strictly QSR-dissipative.LMI-based QSR-dissipative sufficient conditions are established using the linearization system matrices.Second,local input-state strict passivity and local L2-gain,two special forms of local strict QSR-dissipativity,are considered.Finally,for a special nonlinear system,local strict passivity of a switched affine system is investigated according to its linearization.?.Local strict passivity of a switched discrete-time affine nonlinear system is investigated using the linearization technique and the dwell-time dependent storage function method.First,local strict passivity sufficient conditions are established in terms of LMIs.And then,feedback passification of a switched discrete-time affine nonlinear system is addressed when the dynamical system is not locally strictly passive.Furthermore,we give a feedback passification controller design method under the dwell-time dependent state switching.?.Under the framework of dwell time dependent storage function,local strict QSR-dissipativity of switched discrete-time nonlinear systems is studied using the linearization technique,and sufficient conditions are given under which a switched discrete-time nonlinear system is locally strictly QSR-dissipative.Local input-state strict passivity and local l2-gain are also discussed.Furthermore,feedback passi-fication and H? control problem are investigated based on local input state strict passivity and l2-gain,and cont,roller design methods are provided to make a switched discrete-time nonlinear system locally input state strictly passive and have H? per-formance ?,respectively.?.Finite-time passivity of switched nonlinear systems is developed using mul-tiple storage functions method.First,a finite-time passivity concept is proposed,and a switching law is designed to render a switched nonlinear system finite-time passive even if each subsystem is not finite time passive.Second,finite time stability criteria is given in terms of the proposed definition.Finally,finite-time passivity of a feedback connection and a parallel connection of two passive switched systems is addressed.Furthermore,a switching law is designed to make a feedback connection and a parallel connection finite-time passive.?.Passivity-based asymptotical stabilization problem is studied for switched nonlinear systems.When each subsystem is asymptotically zero state detectable and passive on active time intervals,asymptotic stabilization is achieved via co-design of switching laws and controllers.First,we consider stabilization problem of a cascade connection system composed of two passive switched nonlinear systems.An output feedback controller is designed to stabilize the cascade connection if outputs are measurable.Otherwise,a sampled integral stabilization(SIS)technique is employed to investigate asymptotical stabilization of a cascade connection by measuring only the storage function and output of the second switched system.Second,as a special case of a cascade connection,the SIS technique is used to design a feedback controller by sampling the integral of the passive output to stabilize a passive switched nonlinear system with an unmeasurable output.The summaries of the dissertation and prospects for future research are pre-sented in the end of the thesis.