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This note is concerned with the robust stability problem of uncertain two-time-scale systems, where the only information available for system uncertainties is their norm upper bounds. The stability bound /spl epsiv//sup */ is derived via a state transformation and the constructive use of a Lyapunov function. Finally, examples are given to illustrate the applications of the proposed results.

Output feedback control of linear time-invariant singularly perturbed systems is studied. The set of all compensators that stabilize a singularly perturbed system while preserving its two-time-scale structure is parameterized. The parameterization is used to show that any two-frequency-scale stabilizing compensator can be asymptotically approximated by a compensator designed via a sequential procedure. In this procedure, a fast (high-frequency) compensator is designed first to stabilize the fast model of the system. Then, a strictly proper slow (low-frequency) compensator is designed to stabilize a modified slow model. The parallel connection of the two compensators forms a two-frequency-scale stabilizing compensator for the singularly perturbed system.

The block processing technique is applied to a class of two-time-scale linear discrete-time systems. Block state-space structures for slow and fast subsystems have been obtained. Based upon these models, blocked slow and fast controls are designed. In addition, an extra control is designed to exactly compensate for the effects of the parasitics.

The design of stabilizing feedback control of singularly perturbed diserete-time systems is decomposed into the design of slow and fast controllers which are combined to form the composite control. Composite control strategies are developed for the case of single rate measurements (all variables are measured at the same rate) as well as for the case of multirate measurements (slow variables are measured at a rate slower than that of fast variables).

For a class of nonlinear singularly perturbed systems, feedback stabilizing and near-optimal controls are designed using two separate lower order subsystems. The two-time-scale properties greatly simplify the stability analysis and the nonlinear controller design. Two electric machine examples (a dc motor and a synchronous generator) illustrate the proposed design procedure.

Two-time-scale decoupling is adopted to obtain slow and fast subsystems. Based on these subsystems, a multirate composite control strategy is derived. It is shown how a recently presented multirate scheme can be modified to handle slow, nonzero mean disturbances, by introducing time incremental models. The improvements with the given multirate control law are illustrated by an example. >