Adaptive output-feedback stabilisation of an uncertain second-order linear systems

The adaptive stabilisation of uncertain second-order linear systems is addressed, under a lack of information from both states and parameters. The only standard assumptions are no zeros and the sign of the high frequency gain known. To the best of the authors' knowledge, there has been only an explicit solution proposed in the literature so far with proven stability. Despite the simplicity of the system, it does not fit in any of the standard nonlinear control methodologies available. Thus, this work is a complementary contribution providing a mixed control design strategy based on a reduced-order observer, adaptive Immersion & Invariance and Backstepping approaches. Hence, this solution depicts a transversal outlook of those nonlinear control strategies and provides a breakthrough for the generalisation of this non-trivial control problem. Numerical simulations are reported to assess the effectiveness of the adaptive strategy.