This paper presents an improved finite-dimensional linear matrix inequality (LMI) formulation for the &-gain synthesis of a piecewise-affine linear parameter-varying (PALPV) system. The new formulation is then used to design a missile autopilot to investigate issues such as the effectiveness, reliability, and conservatism. Our approach is based on a nonsmooth dissipative systems framework using a continuous, quasi-piecewise-affine parameter-dependent Lyapunov function (QPAL) which has been shown to yield a less conservative, guaranteed result than previously published techniques based on quasi-affine parameter-dependent Lyapunov functions (QALs) or Lurb-Postnikov Lyapunov functions. The results in this paper improve the computational efficiency by using a different “convexifying” technique. We also generalize our previous results by eliminating the restriction on the number of parameters.