Exponential stabilization of uncertain linear systems with delays on state and control input

Robust exponential stabilization of linear uncertain d systems with delays on state and control input is studied in this paper. Based on the Lyapunov-Krasovskii method, we establish new criteria that ensure the exponential and asymptotical robust stability of the closed-loop system with memoryless state feedback controller. The criteria are derived in terms of matrix inequalities, which can be easily solved by efficient convex optimization algorithms. By comparing with the recent results, we show that our results are less conservative than those in the literature. where x(t) 2 Rn is the state, u(t) 2 Rm is the control, A,A1,B,B1 are given matrices, and �(�) 2 C(( h,0), Rn). The time-varying parameter uncertaintiesA(t), �A1(t), �B(t), �B1(t) are assumed to be in the form �A(t) = D1F1(t)E1, �B(t) = D2F2(t)E2, �B1(t) = D3F3(t)E3, �A1(t) = D4F4(t)E4,