| Switched systems,which can accurately describe the phenomenon of multi-model switching and multi-controller switching in actual engineering problems,are a hot spot in the control field,and many foundational results have been achieved in stability analysis.The systems in the real world have more or less nonlinear characteristics,and thus the study on nonlinear switched systems has the significance for theory and practical applications.In the past 30 years,port-controlled Hamilton(PCH)systems as an important class of nonlinear systems with wide practicability,have made many breakthroughs in stabilization and H? control.However,the research on switched PCH systems has been concerned for a long time while developed slowly.On the other hand,unstable modes are often encountered in practical systems.In recent years,they have become the focus in the switched systems community.However,due to the complexity of nonlinear systems themselves,there are still many problems to be solved in the analysis and control of nonlinear switched systems with unstable modes.This dissertation systematacially addressed the analysis and control problems for several switched PCH systems by energy-based multiple Lyapunov functions(MLFs)methods and time-dependent switching strategies.Further,based on the proposed switching strategies,combined with the multiple discontinuous Lyapunov functions(MDLFs)methods,the problems of stability and disturbance attenuation are studied for switched nonlinear systems with unstable modes.The research contents of the dissertation are divided into six parts as follows:1.The problems of the stability,stabilization and H? control are addressed for switched PCH systems.For autonomous switched PCH systems with all stable modes,by the energy-based MLFs method,sufficient conditions of both exponential stability and asymptotical stability are obtained under arbitrary switching signals with an average dwell time scheme.Then,based on state feedback control strategies,the mode-dependent controllers are designed to stabilize switched PCH systems,and the mode-dependent H? controllers are presented to attenuate the disturbances for switched PCH systems,while switched PCH systems are subject to actuator saturation(AS),the stabilization and H? control are investigated and the truncation-inequality method is employed to deal with the saturation.(Chapter 2 in the dissertation)2.The stabilization and H? control are studied for switched PCH systems with unstable modes.By designing a class of quasi-alternative switching signals and mode-dependent state feedback controllers,the stabilization criteria are given for switched PCH systems with unstable modes via the energy-based MLFs method and slow/fast mode-dependent average dwell time(MDADT)switching strategies.Furthermore,when the disturbances are considered,by revealing the internal relationship between slow switching and fast switching and defining a class of indicative functions,the sufficient conditions of H? control are achieved for the considered system by the mode-dependent state feedback control strategies and the proposed slow/fast MDADT switching scheme.In addition,when the considered system is subject to AS,based on the obtained results,the sufficient conditions of stabilization and H? control are given for the systems with AS by the truncation-inequality technique.(Chapter 3 in the dissertation)3.In the designed slow/fast switching scheme above,the MDADT of the fast switching scheme is limited by upper bounds.To solve the problem,the stabilization and H?control problems are studied for switched PCH systems with unstable modes again,where a MDADT-based ratio tradeoff switching strategy is developed by a time subsequence technique to harmonize the running time of the asymptotic stable modes and the other ones.Firstly,based on the mode-dependent state feedback controllers,the stabilization conditions are given for switched PCH systems with unstable modes under the improved ratio tradeoff switching scheme.Secondly,for the case that there are disturbances for the system,the mode-dependent H? controllers are designed to attenuate the disturbances,besides,the H? control conditions are obtained for the system by energy-based MLFs method combined with the proposed switching scheme.In the proposed switching scheme,the running time of all the modes only needs to satisfy the ratio tradeoff condition,while it is no longer restricted by upper bounds.(Chapter 4 in the dissertation)4.Finite-time stabilization and H? control for a class of switched PCH systems subject to AS with all unstable modes.Firstly,based on the energy-based MLFs method and the MDADT switching strategies,the sufficient conditions are established for autonomous switched PCH systems,where all the modes of the system are unstable over an infinite time interval but finite-time stable in the fixed time interval.Secondly,based on the finite time stability result,the finite-time stabilization conditions are obtained for switched PCH systems with AS by the mode-dependent state feedback control strategies and the truncation-inequality technique.Finally,the mode-dependent state feedback controllers are designed to attenuate the disturbances for switched PCH systems with AS and disturbances,and the criterion is presented to solve the finite-time H? control for the considered system.(Chapter 5 in the dissertation)5.Stability and weighted l2-gain analysis are addressed for discrete-time switched nonlinear systems with unstable modes via slow/fast switching strategies.By introducing a class of alternative switching signals and using MDLFs methods,the stability criteria are established for discrete-time switched nonlinear systems with unstable modes via slow/fast MDADT switching scheme,where the MDADT has the tighter bounds in the proposed switching scheme.Furthermore,when the disturbances are considered in the system,by exploring the relationship between slow switching and fast switching,the sufficient conditions of weighted l2-gain are obtained based on the proposed switching scheme.Meanwhile,the stability and weighted l2-gain conditions are also given for discrete-time switched linear systems with unstable modes by the quadratic MDLFs method and the obtained slow/fast MDADT switching scheme.(Chapter 6 in the dissertation)6.The analysis on stability and weighted L2-gain is studied for switched nonlinear systems with unstable modes via inequality tradeoff switching strategies.Firstly,a MDADT-based inequality tradeoff switching strategy is designed by a time subsequence technique.Further,based on the MDLFs method,the sufficient conditions on stability and weighted L2-gain are established for switched nonlinear systems with unstable modes,where the inequality tradeoff switching scheme with tighter bounds is obtained.Moreover,based on the proposed results,the stability and weighted L2-gain criteria are also given for switched linear systems with unstable modes by quadratic MDLFs methods.It should be pointed out that the proposed analysis approach and switching strategy can be applied to study discrete-time switched systems with unstable modes.In addition,the MDADT on unstable modes is not restricted by upper bounds in the proposed switching scheme,and different from ratio tradeoff switching scheme,the inequality tradeoff switching scheme can also be suitable for switched systems with all stable modes.(Chapter 7 in the dissertation). |
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