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For a general type of nonlinear tracking problem, we consider gain scheduling based on a family of linear dynamic controller designs for a family of plant linearizations about constant operating points. Necessar and sufficient conditions for existence of gain schedulel controllers satisfying appropriate requirements are presented. Using these conditions, the impact of linear controller configuration on existence of a gain scheduled controller is discussed.

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In this paper, we treat the fundamental problem of state estimation for a class of linear impulsive systems with time-driven impulsive effects. We show that a strong observability property enables an impulsive observer to be constructed that yields uniformly exponentially stable estimation error dynamics. This approach accommodates impulsive systems with arbitrarily-spaced impulse times and singular state transition matrices in a manner reminiscent of well-known results for time-varying discrete-time linear systems. As an example, an observer is constructed for an impulsive system that produces general cubic spline signals.