LQG Controller Synthesis with Noise Spectral Uncertainties and Nonlinear Time-varying Perturbations

The problem of robust controller synthesis with noise spectral uncertainties and nonlinear time-varying perturbations in the LQG (linear-quadratic-Gaussian) optimal systems is considered. A robust stabilization criterion is derived for multivariable stochastic systems with nonlinear time-varying perturbations. We frame up an algorithm for synthesizing the robust controller not only to minimize the least favorable cost functional J but also to satisfy the robust stabilization criterion via specifying two weighting matrices Q and R. The Wiener- Hopf's technique in the LQG optimal system, the saddle point theory and a property of the contractive operator are employed to treat the problem. Furthermore, there are no stable, proper or minimum phase constraints on the controlled plant.