Robust Stabilization Analysis

both in state and control are discussed. A stabilization criterion is obtained to guarantee the quadratic stability of the closed-loop system. The controller gain matrix is included in an Hamiltonian matrix, which is easily constructed by the boundedness of the uncertainties.
Key words uncertainty; robust stabilization; state feedback; quadratic stabilization

Many techniques have been proposed to stabilize uncertain systems with state delay via state feedback in Ref.[1~12], LI et al. investigated the approach of linear matrix inequality (LMI) [1,5], Mori, Su et al. discussed the robust stabilization where the uncertainty satisfies the so-called matching conditions, by using the property of LMI[2,3]. Perterson et al. introduced a Ricatti equation approach[6], Hoi, Shen et al., designed the state feedback controller to stabilize the uncertain dynamic systems with invariant or time-varying delays, where the uncertain dynamic system does not satisfy matching-conditions, but it is not easy to solve the Ricatti equation due to multiple parameters in the equation[7,8]. All those approaches are sufficient, that is, the controllers are included in LMIs or Ricatti Equations derived from some sufficient conditions. This paper discusses the stabilization problem of uncertain systems with time-delays, a new sufficient criterion is obtained. For some systems, the state feedback controller to quadratically stabilize the uncertain dynamics can be easily obtained by solving an Hamiltonian matrix, not using LMI or Ricatti equation approach to obtain it.