Summary This paper considers the design of simultaneous static output feedback controllers for a finite collection of time‐delay linear systems. By solving a minimization problem, we try to find an output feedback low‐gain controller such that all resultant closed‐loop time‐delay systems are internally stable and satisfy a prespecified H∞‐norm requirement. Based on the barrier method, necessary conditions for local optimum of the minimization problem are derived. An example is given for illustration.

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Based on the discrete affine wavelet transforms, we develop a new "basis" for wavelet networks for better approximating non-smooth nonlinear functions. It is shown that the wavelet formalism supports a theoretical framework, and it is possible to perform both analysis and synthesis of feedforward neural networks. Using the spatio-spectral localization properties of wavelets, we can synthesize a feedforward network to reduce the training problem to one of convex optimization problem.Specifically, we have developed the algorithm for approximation of high-dimensional nonlinear functions. Finally, the inverted pendulum stabilizing problem is studied via the proposed wavelet neural networks in order to illustrate the usefulness of the developed theoretical framework. -Definition 2.1[7l : A sequence of vectors [ qJ,=., in a Hilbert space H is called a frame if there exists A>O, Beso that, for all f in H, J We call A and B the frame bounds. Definition 2.2[10] : If {(p,] is a frame in H, then the frame operator S is the linear operator from H to H defined by 0-7803-21 14-6/94/$4.00 0 1994 IEEE.