Abstract
In this paper, for the input-state-output class of port-Hamiltonian systems the contraction property is characterized. Recently, some results on contraction of port-Hamiltonian systems with constant interconnection and damping matrices have been published. This paper, extends these results for state-modulated interconnection and damping matrices. In this regard, the powerful method of IDA-PBC is extended for tracking designs. Controller design for under-actuated mechanical systems with non-constant mass matrices usually leads to non-constant (state-modulated) interconnection and damping matrices for the closed-loop system. Therefore, the result of this paper can be used for tracking controller design for under-actuated mechanical systems. To show the potency of proposed results, a tracking controller for cart-pole system is designed and simulated.
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