New LMI Formulation For Observed-State Feedback Stabilization

Based on recent results on homogeneous polynomially parameter-dependent (HPPD) solutions to parameter-dependent LMIs (PD-LMIs), we investigate a new LMI formulation for an observed-state feedback comprising of matrix-valued HPPD functions of degree g, deriving a testable LMI condition that is sufficient and asymptotically necessary to existence of a quadratic Lyapunov function assuring quadratical stability. The main contribution of this paper is that the families of finite-dimensional LMI are parameterized in term of the polynomial degree d. As d increases, more and more sufficient LMI conditions are generated, being easier satisfied due to more freedom provided by the new variables involved. An example using new designs to illustrate the LMI relaxation is provided.