paper presents a practical design perspective on multivariable feedback control problem. It reviews the basic issue-feedback design in the face of uncertainties-and generalizes known single-input, singleoutput (SISO) statements and constraints of the design problem to multiinpat, multioutput ("0) c a s e s. Two major " 0 design a p proaches are then evaluated in the context of these resul ts. research was supported by the ONR under Contract NOOO14-75-C-0144, Manuscript received March 13, 1980; revised October 6, 1980. This by the DOE under Contract ET-78-C-01-3391, and by NASA under Grant NGL-22-009-124.

This paper examines the robustness properties of existing adaptive control algorithms to unmodeled plant high-frequency dynamics and unmeasurable output disturbances.It is demonstrated that there exist two infinite-gain operators in the nonlinear dynamic system which determines the time-evolution of output and parameter errors. The pragmatic implication of the existence of such infinite-gain operators is that (a) sinusoidal reference inputs at specific frequencies and/or (b) sinusoidal output disturbances at any frequency (including d.c.), can cause the loop gain to increase without bound, thereby exciting the unmodeled high-frequency dynamics, and yielding an unstable control system. Hence, it is concluded that existing adaptive control algorithms cannot be used with confidence in practical designs, because instability can result with high probability.

No abstract

Abstract-This paper provides a tutorial overview of the LQG/LTR design procedure for linear multivariable feedback systems. LQWLTR is interpreted as the solution of a specific weighted H*-tradeoff hetween transfer functions in the frequency domain. Properties of this solution are examined for both minimum-phase and nonminimum-phase systems. This leads to a formal weight augmentation procedure for the miuimumphase case which permits essentially arbitrary specification of system sensitivity functions in terms of the weights. While such arbitrary specifications are not possible for nonminimum-phase problems, a direct relationship between weights and sensitivities is developed for nonminimum-phase SlSO and certain nonminimum-phase MIMO cases which guides the weight selection process.