On the adaptive stabilization of MIMO systems with uncertain control direction

This paper addresses the problem of adaptive stabilization of MIMO systems whose constant high-frequency gain matrix is nonsingular but has completely unknown sign structure. Unlike most existing approaches, no positivity, symmetry, or diagonal dominance assumptions on the gain matrix are required. Building upon the unit-vector framework and the concept of unmixing sets, a modified discontinuous adaptive control strategy is proposed. The key novelty consists in decoupling the mechanism that cycles through the elements of the unmixing set from the adaptation of the control input magnitude. In particular, the adaptive gain is used exclusively to govern the switching among candidate gain matrices, while the control input magnitude is fixed a priori. A Lyapunov-based analysis proves global asymptotic stabilization for driftless systems. The results are further extended to systems affected by matched bounded disturbances under mild additional assumptions. Simulation studies illustrate the effectiveness of the proposed approach and highlight its advantages in terms of reduced control authority and alleviated transient peaking.