Robust lqg optimal controller design for multivariable discrete saturating systems with noise spectral uncertainties and non-linear time-varying unmodelled dynamics

A design procedure is proposed for robust linear-quadratic-gaussian (LQG) optimal controller synthesis against noise spectral uncertainties, non-linear time-varying (NLTV) unmodelled dynamics in discrete saturating systems. A robust stability criterion is derived for multivariable stochastic discrete-time systems with NLTV unmodelled dynamics and constrained actuators. An algorithm based on the robust stabilization creterion is presented for synthesing a robust controller not only to minimize the least favourable cost functional 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 the Nevanlinna-Pick interpolation theory. The Wiener Z-domain solution for controller synthesis, the saddle point theory, and the properties of Schur operator (Class S) are employed to treat this problem. Finally, a numerical example is given to illustrate the results.