In this paper, we present a delay-dependent robust model predictive control (MPC) algorithm for a class of discrete-time linear state-delayed systems subjected to polytopic-type uncertainties and input constraints. The state-feedback MPC law is calculated by minimizing an upper bound of the worst-case quadratic cost function over an infinite time horizon at each sampling instant. In contrast to existing robust MPC techniques, the main advantage of the proposed approach is that the algorithm is derived by using a descriptor model transformation of the time-delay system and by applying a result on bounding of cross products of vectors. This has significantly reduced the conservativeness. It has been shown that robust stability of the closed-loop system is guaranteed by the feasible MPC from the optimization problem. The effectiveness of the algorithm is demonstrated by a simulation.
I. INTRODUCTIONIME-delay often occurs in many dynamical systems, such as chemical processes, transportation systems, and communication networks etc. Time-delay often leads to serious deterioration of system stability and performance. Moreover, since it is difficult to obtain the exact model of system dynamics, thus uncertainties are unavoidable. Therefore, robust control of uncertain time-delay systems has received much attention, and many research results have been reported in control literature (see [1][2][3][4]). There are mainly two types of stabilization results: one is delay-independent and the other is delay-dependent. It has been shown that delay-dependent results taking into account the size of delays are generally less conservative than delay-independent ones, which do not include any information on the size of delays.Most of the literatures on time-delay systems have neglected input constraints, which normally represent physical limits (such as valve saturation and power limitations, etc) and widely exist in many processes. A well method with ability to handle constraints on input /output is the MPC [5] .
The practical stabilization problem is investigated for a class of linear systems with actuator saturation and input additive disturbances. Firstly, the case of the input additive disturbance being a bounded constant and a variety of different situations of system matrices are studied for the three-dimensional linear system with actuator saturation, respectively. By applying the Riccati equation approach and designing the linear state feedback control law, sufficient conditions are established to guarantee the semiglobal practical stabilization or oscillation for the addressed system. Secondly, for the case of the input additive disturbances being time-varying functions, a more general class of systems with actuator saturation is investigated. By employing the Riccati equation approach, a low-and-high-gain linear state feedback control law is designed to guarantee the global or semiglobal practical stabilization for the closed-loop systems.
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