The guaranteed cost control problem for a continuous-time uncertain singular system with state and control delays, and a given quadratic cost function is studied in this paper. Sufficient conditions for the existence of the guaranteed cost controller are derived based on the linear inequality (LMI) approach. A parameterized characterization of the guaranteed cost laws is given in terms of the feasible solutions to a certain LMI, and the cost function of guaranteed cost controller exists an upper bound.
Hai Zhang 1,2 , Wei Jiang 1 , Jun Du 1,3 (1. School of Mathematical Sciences, Anhui University, Hefei 230039, 2. School of Math. and Computation Science, Anqing Teachers College, Anqing 246011, Anhui
The global exponential stability of the zero solution to a class of differential system with delay is considered. By constructing a suitable type of Lyapunov functional and using some analytical techniques, we derive some criteria to check exponential stability of this system. The results establish a relation between the delay time and the parameters of the system. Two examples are also given to illustrate the validity of the results.
