Output Regulation for Unknown Stable Linear Systems

The regulation problem is addressed for single-input, single-output, linear unknown stable systems P(s), of unknown order, with exosystems generating biased multi-sinusoidal references and/or disturbances containing at most q known frequencies ω_i, 1 ≤ i ≤ q. Sufficient conditions are presented which require the knowledge of sign[P(0)] and either sign{Re[P(jω_i)]} or sign{Im[P(jω_i)]}, 1 ≤ i ≤ q. The constructive proofs lead to the design of regulators with minimal order (2q + 1), provided that the gains are sufficiently small. For stable plants P(s) such that Re[P(jω)] > 0, for any ω ∈ ℝ, a universal modular regulator is designed without gain limitations.