Linear Matrix Inequality Based Static Output Feedback Sliding Mode Control for Discrete Time Systems

This paper discusses the design of a static output feedback based sliding mode controller for MIMO non-minimum phase discrete time systems. In previous work, it was shown that by identifying a minimal set of current and past outputs to determine an extended output signal, an augmented system can be obtained which permits the design of a sliding manifold based upon output information only, which renders the sliding mode dynamics stable. In this paper, it is shown that if the extended outputs chosen span the state zero directions of an invariant zero of the system, then the invariant zero disappears from the augmented system. Linear matrix inequalities are then used for sliding surface design. Such controllers have great potential within reconfigurable control schemes for application in the presence of multiple sensor failures. The methodology is applied to an aircraft system to show the efficacy of the design philosophy.