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 addresses the stabilization of nonlinear systems,which is represented by a Takagi–Sugeno (T-S) model. Based on the extendednonquadratic Lyapunov function and the nonparallel distributedcompensation law, three new results are obtained by using appropriateslack matrices, collection matrices, and the higher dimensional collectionmatrix. The first two results are less conservative, and computationally lessexpensive, than some of the existing results. The third result combines theprocedures of the first two results, and is less conservative, but is computationallymore expensive than the first two results. The effectiveness of thenew results is validated by two numerical examples

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 paper addresses robust model predictive control (MPC) for time-delay systems with polytopic uncertainty.Uncertain time-varying input delay and state delays are considered, and the infinite horizon control moves areparametrised into an augmented state feedback law at each time instant. A receding horizon implementation ofthis state feedback law renders satisfaction of input/state constraints and closed-loop stability. For time-invariantdelays and known delays, simplified results are obtained. A numerical example and a benchmark problem oncontinuous stirred tank reactor (CSTR) are given to illustrate the effectiveness of the proposed techniques.

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.