This paper presents an H∞ controller design method for piecewise discrete time linear systems based on a piecewise quadratic Lyapunov function. It is shown that the resulting closed loop system is globally stable wit...This paper presents an H∞ controller design method for piecewise discrete time linear systems based on a piecewise quadratic Lyapunov function. It is shown that the resulting closed loop system is globally stable with guaranteed H∞ performance and the controller can be obtained by solving a set of bilinear matrix inequalities. It has been shown that piecewise quadratic Lyapunov functions are less conservative than the global quadratic Lyapunov functions. A simulation example is also given to illustrate the advantage of the proposed approach.展开更多
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
This paper addresses the stability problem for a class of switched nonlinear time varying delay systems modeled by delay differential equations. By transforming the system representation under the arrow form and using...This paper addresses the stability problem for a class of switched nonlinear time varying delay systems modeled by delay differential equations. By transforming the system representation under the arrow form and using a new constructed Lyapunov function,the aggregation techniques,the Borne-Gentina practical stability criterion associated with the properties, new delay-independent stability conditions of the considered systems are established. Compared with the existing results in this area, the obtained result is explicit, simple to use and allows us to avoid the problem of searching a common Lyapunov function. Finally, an example is provided, with numerical simulations,to demonstrate the effectiveness of the proposed method.展开更多
文摘This paper presents an H∞ controller design method for piecewise discrete time linear systems based on a piecewise quadratic Lyapunov function. It is shown that the resulting closed loop system is globally stable with guaranteed H∞ performance and the controller can be obtained by solving a set of bilinear matrix inequalities. It has been shown that piecewise quadratic Lyapunov functions are less conservative than the global quadratic Lyapunov functions. A simulation example is also given to illustrate the advantage of the proposed approach.
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.
文摘This paper addresses the stability problem for a class of switched nonlinear time varying delay systems modeled by delay differential equations. By transforming the system representation under the arrow form and using a new constructed Lyapunov function,the aggregation techniques,the Borne-Gentina practical stability criterion associated with the properties, new delay-independent stability conditions of the considered systems are established. Compared with the existing results in this area, the obtained result is explicit, simple to use and allows us to avoid the problem of searching a common Lyapunov function. Finally, an example is provided, with numerical simulations,to demonstrate the effectiveness of the proposed method.
