The control synthesis for switched systems is extended to distributed parameter switched systems in Hilbert space. Based on semigroup and operator theory, by means of multiple Lyapunov method incorporated average dwel...The control synthesis for switched systems is extended to distributed parameter switched systems in Hilbert space. Based on semigroup and operator theory, by means of multiple Lyapunov method incorporated average dwell time approach, sufficient con- ditions are derived in terms of linear operator inequalities frame- work for distributed parameter switched systems. Being applied to one dimensional heat propagation switched systems, these lin- ear operator inequalities are reduced to linear matrix inequalities subsequently. In particular, the state feedback gain matrices and the switching law are designed, and the state decay estimate is explicitly given whose decay coefficient completely depends on the system＇s parameter and the boundary condition. Finally, two numerical examples are given to illustrate the proposed method.展开更多
The present paper is concerned with stability and L_(2) gain analysis of switched distributed parameter system(SDPS)with time delay.First,exponential stability is discussed,and the state decay estimate of the system i...The present paper is concerned with stability and L_(2) gain analysis of switched distributed parameter system(SDPS)with time delay.First,exponential stability is discussed,and the state decay estimate of the system is explicitly given by using linear matrix inequalities(LMIs)incorporating with the average dwell time(ADT)method.Second,L_(2) gain analysis is also studied.At last,illustrative examples are given to show the effectiveness of the proposed method.The main contribution of the paper is:some criteria of exponential stability and L_(2) gain for multiple-input multiple-output(MIMO)switched PDE are developed in the form of LMIs and ADT signal for the first time.The advantage of the work is we generalize the application range of the related research.The proposed method is expected to provide an effective tool for stability and H∞control analysis of SDPS.展开更多
基金supported by the National Natural Science Foundation of China(6127311961374038+2 种基金6147307961473083)the Natural Science Foundation of Shanxi Province(2012011002-2)
文摘The control synthesis for switched systems is extended to distributed parameter switched systems in Hilbert space. Based on semigroup and operator theory, by means of multiple Lyapunov method incorporated average dwell time approach, sufficient con- ditions are derived in terms of linear operator inequalities frame- work for distributed parameter switched systems. Being applied to one dimensional heat propagation switched systems, these lin- ear operator inequalities are reduced to linear matrix inequalities subsequently. In particular, the state feedback gain matrices and the switching law are designed, and the state decay estimate is explicitly given whose decay coefficient completely depends on the system＇s parameter and the boundary condition. Finally, two numerical examples are given to illustrate the proposed method.
基金This work was supported by the China Scholarship Council Fund(No.201808140223)the National Natural Science Foundation of China(No.11661020).
文摘The present paper is concerned with stability and L_(2) gain analysis of switched distributed parameter system(SDPS)with time delay.First,exponential stability is discussed,and the state decay estimate of the system is explicitly given by using linear matrix inequalities(LMIs)incorporating with the average dwell time(ADT)method.Second,L_(2) gain analysis is also studied.At last,illustrative examples are given to show the effectiveness of the proposed method.The main contribution of the paper is:some criteria of exponential stability and L_(2) gain for multiple-input multiple-output(MIMO)switched PDE are developed in the form of LMIs and ADT signal for the first time.The advantage of the work is we generalize the application range of the related research.The proposed method is expected to provide an effective tool for stability and H∞control analysis of SDPS.
