The stabilization of a network controlled system including a global time-varying delay is investigated in this note. This delay is considered to be unknown but it is assumed that a bounded error estimate is available. The exponential uncertainty induced by the time-varying delay is decomposed into a sum of a polytopic term and an uncertain bounded term. Sufficient conditions to design a dynamic output feedback controller depending on estimate of the time-varying delay are proposed as LMIs. An illustration shows how our methodology enlarges the design techniques of the literature.

Summary This paper focuses on the synthesis of sampled‐data linear parameter‐varying (LPV) control laws. In particular, the problem of L2 disturbance attenuation for continuous‐time LPV systems under aperiodic sampling is addressed. It is explicitly assumed that the LPV controller is updated only at the sampling instants while the plant parameter can evolve continuously between two sampling instants. The proposed approach is based on a polytopic model for the LPV system and the use of a parameter‐dependent looped‐functional to deal with the aperiodic sampling effects. From these ingredients, conditions in a quasi‐LMI form (ie, they are LMIs provided a scalar parameter is fixed) are derived to compute a stabilizing control law ensuring an upper bound on the closed‐loop system L2‐gain. These conditions are then incorporated to convex optimization problems aiming at either minimizing the L2‐gain upper bound or maximizing the allowable sampling interval for which stability is ensured. Numerical examples illustrate the proposed methodology.

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In this paper, we assume that a set of non preemptive controller tasks should be implemented on a limited computational resource platform, and look for a sampling period assignment that allows to obtain the desirable performance. The problem is formulated as a multi-objective optimization problem under a resource constraint, where the cost functions depend on the sampling period. Linear-quadratic controllers are used, resulting on feedback gains that also depend on the sampling period. The global cost function is chosen as a weighted sum of all plants performances, translating the multiobjective optimization problem into a single-objective one which provides an additional degree of freedom and leads to a set of solutions denoted as Pareto efficient. To handle this additional variable, we assume a Nash bargaining cooperative game. An upper level task performs the update of the sampling period and of the plant input, to be used on a finite-horizon control strategy, for each control loop. A numerical example is provided to illustrate our approach.

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