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This paper proposes a new design and practical implementation of a robust <inline-formula> <tex-math notation="LaTeX">${\mathcal H}_{\infty }$ </tex-math></inline-formula> control applied to some mechanical systems considering in the controller design full access to the state variables and in the equivalent controller implementation only the feedback of all positions or of all velocities of the plant. An important characteristic, though, is that limitations are considered for the state feedback. Two methods are presented, one that uses feedback only from state variables related to positions of the system and another that uses feedback only from state variables related to velocities. The control strategy is based on Linear Matrix Inequalities (LMIs), using the theory of <inline-formula> <tex-math notation="LaTeX">$\mathcal D$ </tex-math></inline-formula>-stability, which allows the designer to allocate the closed loop system eigenvalues in a negative complex semi-plane region, which, in addition to ensuring stability, also allows to attend certain performance requirements of the feedback system. The paper motivation is to provide satisfactory control results with limited states access, without any kind of estimation of the state variables that are not available. Therefore, the proposed control systems are interesting options as alternatives for the design of full-order state feedback for plants with uncertain parameters using only output feedback, considering that it is not required to build an observer to estimate any plant state variable. Furthermore, their implementations are relatively cheaper because it is not necessary to measure all state variables of the plant.

Implementations of Full State Feedback Robust Control Designs for Mechanical Systems Using Only Positions or Velocities Output Feedback