This paper addresses the synthesis approach for output feedback robust model predictive control for systems with polytopic description, bounded state disturbance and measurement noise. Off-line, it calculates a sequence of output feedback laws based on the state estimators, by solving linear matrix inequality (LMI) optimization problems. On-line, at each sampling time, it chooses an appropriate output feedback law from this sequence.The primary contribution is to present a rigorous method to guarantee satisfaction of input/state constraints. A numerical example is given to illustrate the effectiveness of the controller.

This paper gives two alternative off-line synthesis approaches to robust model predictive control (RMPC) for systems with polytopic description. In each approach, a sequence of explicit control laws that correspond to a sequence of nested asymptotically invariant ellipsoids are constructed off-line. In order to accommodate a wider class of systems, nominal performance cost is chosen to substitute the "worst-case" one in an existing technique. In the design of control law for a larger ellipsoid, the second approach further incorporates the knowledge of control laws associated with all smaller ellipsoids, so as to further improve feasibility and optimality. The effectiveness of the alternative approaches is illustrated by a simulation example.

This paper further studies stabilization of nonlinear systems represented by a Takagi–Sugeno (T-S) discrete fuzzy model. By extending a nonquadratic Lyapunov function and applying a nonparallel distributed compensation (non-PDC) law, a new stabilization conclusion is presented that is a generalization of some previous results in the literature. The new conclusion under a special situation is also suitable for a PDC law, which presents to be more relaxed than some existing results. An example is provided to demonstrate the effectiveness of the new conclusions.

With Kleinman's controller, its extended form and Riccati iteration as analyzing tools, the stability of GPC under various parameter cases is discussed. The overall closed-loop stability conclusions of GPC in equivalence with Kleinman's controller are obtained, which cover some existing results and provide the theoretical foundation for stable design of predictive control.

This article addresses the robust model predictive control (MPC) for systems with polytopic uncertaintydescription. In the case of multiple state delays, some results are given in the previous works. However, previousworks are not well established for input-delay systems. This article proposes new approaches that can effectivelyhandle not only the input-delay, but also the multiple delayed input. For the time-delay system, a general MPCsolution is based on the use of augmented delay-free state-space description, which can be computationallyexpensive. Hence, in general there are simplified formulations based on the time-delay description, which can beapplied in different situations. This article proposes three simplified formulations, with the first incorporating aprevious result as a special case, the second being a solution for a unique class of systems and the third being amore general solution without special assumptions on the plant. Numerical examples illustrate the effectivenessof the proposed approaches.