Robust LQG optimal controller design for multivariable discrete saturating systems with noise spectral uncertainties and nonlinear time-varying unmodeled dynamics

A design procedure is proposed for robust LQG (linear-quadratic-Gaussian) optimal controller synthesis against noise spectral uncertainties, nonlinear time-varying (NLTV) unmodeled dynamics in discrete saturating systems. A robust stability criterion is derived for multivariable stochastic discrete-time systems with NLTV unmodeled dynamics and constrained actuators. An algorithm based on the robust stabilization criterion is presented for synthesizing a robust controller not only to minimize the least favorable cost functional J but also to satisfy the robust stabilization criterion by specifying an appropriate weighting scalar in the cost functional. A necessary and sufficient condition for the solvability of such a robust stabilization problem is derived by means of Nevanlinna-Pick interpolation theory. The Weiner Z-domain solution for controller synthesis, the saddle point theory, and the properties of the Schur operator (Class S) are employed to treat this problem. Finally, a numerical example is given to illustrate the results.