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This paper is concerned with the ℋ∞ model reduction for linear parameter-varying (LPV) systems with both discrete and distributed delays. For a given stable system, our attention is focused on the construction of reduced-order models, which approximate the original system well in an ℋ∞ norm sense. First, a sufficient condition is proposed for the asymptotic stability with an ℋ∞ performance of the error system by using the parameter-dependent Lyapunov functional method. Then, the decoupling technique is applied, such that there does not exist any product term between the Lyapunov matrices and the system matrices in the parametrised linear matrix inequality (PLMI) constraints; thus a new sufficient condition is obtained. Based on the new condition, two different approaches are developed to solve the model reduction problem. One is the convex linearisation approach and the other is the projection approach. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed design method.

In the chain scattering framework, it has been shown in Lee and Soh (2004) that the problem of simultaneous stabilization of a finite collection of l linear time-invariant plants such that each closed-loop transfer function has an norm less than a prescribed performance level is equivalent to a simultaneous strongly stabilizing problem, i.e. finding a single stable and norm bounded controller for associated l − 1 unimodular plants such that each resulting closed-loop system is stable and norm bounded. This paper attempts to provide a solution to the simultaneous strongly stabilization problem. A new sufficient condition in the form of the solution to only one algebraic Riccati equation is provided for the existence of a strongly stabilizing controller for a given stable system obtained from the parameterization of stabilizing controllers. With the parameterization of strongly stabilizing controllers provided in this paper, a solution is given for the simultaneous strongly stabilization problem and hence, ...

A generalized predictive controller (GPC) is derived based on a general state-space model. The equivalence of the predictive control problem to a perturbation problem is revealed. In the case of a small perturbation, the closed-loop poles are calculated with high accuracy. For the case of a general perturbation, an upper bound on the permissible perturbation norm is derived assuming an open-loop stable system. Both the plant-model match and plant-model mismatch cases are analysed. The controller is proven to be robust and an adaptive implementation is motivated. For open-loop stable systems, the convergence and stability of the control scheme are ensured by proper tuning of the control weight and prediction horizon. The results are applicable to a wide range of predictive controllers. The main contribution of this paper is not a new control algorithm, but new techniques to analyse the GPC as well as new stability and convergence results.

A suboptimal selection of observation times is considered which minimizes the quadratic control performance in the control and state error under a restricted number of observations. Two convenient observation algorithms are proposed for multiple available observations based upon the analytical results obtained for a continuous system, i.e. a periodic observation policy for an unstable system, and its modified versions, taking into account the transient state, for a -stable system.