The robust exponential stabilization problem for uncertain systems isstudied. Based on the solution for a nominal linear quadratic regulator problem with a prescribeddegree of stability, the methods of constructing st...The robust exponential stabilization problem for uncertain systems isstudied. Based on the solution for a nominal linear quadratic regulator problem with a prescribeddegree of stability, the methods of constructing state feedback controllers are developed to ensurethe robust stability of the closed loop system under the conditions weaker than the matchingcondition. Also, the cases where the matching condition is satisfied are considered in detail. Someexamples are included to show the solution methods.展开更多
In this paper we study the asymptotic behavior of global classical solutions to the Cauchy problem with initial data given on a semi-bounded axis for quasilinear hyperbolic systems. Based on the existence result on th...In this paper we study the asymptotic behavior of global classical solutions to the Cauchy problem with initial data given on a semi-bounded axis for quasilinear hyperbolic systems. Based on the existence result on the global classical solution, we prove that, when t tends to the infinity, the solution approaches a combination of C1 travelling wave solutions with the algebraic rate （1 ＋ t）^-u, provided that the initial data decay with the rate （1 ＋ x）^-（l＋u） （resp. （1 - x）^-（1＋u）） as x tends to ＋∞ （resp. -∞）, where u is a positive constant.展开更多
基金This work was financially supported by the National Science Foundation of China(No.19971088).
文摘The robust exponential stabilization problem for uncertain systems isstudied. Based on the solution for a nominal linear quadratic regulator problem with a prescribeddegree of stability, the methods of constructing state feedback controllers are developed to ensurethe robust stability of the closed loop system under the conditions weaker than the matchingcondition. Also, the cases where the matching condition is satisfied are considered in detail. Someexamples are included to show the solution methods.
基金Supported by the National Natural Science Foundation of China (Grant No.10771038)
文摘In this paper we study the asymptotic behavior of global classical solutions to the Cauchy problem with initial data given on a semi-bounded axis for quasilinear hyperbolic systems. Based on the existence result on the global classical solution, we prove that, when t tends to the infinity, the solution approaches a combination of C1 travelling wave solutions with the algebraic rate （1 ＋ t）^-u, provided that the initial data decay with the rate （1 ＋ x）^-（l＋u） （resp. （1 - x）^-（1＋u）） as x tends to ＋∞ （resp. -∞）, where u is a positive constant.
