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.

This paper considers stability of discrete-time nonlinear systemsin Takagi–Sugeno (T–S) form. This problem has been studied formore than 20 years with many sufficient conditions, and the asymptoticallynecessary and sufficient (ANS) conditions with respect to the commonquadraticLyapunov, function, having being obtained. This paper considersgeneral forms of homogeneous polynomially nonquadratic Lyapunov(HPNQL) function and homogeneous polynomially parameterized nonparalleldistributed compensation (HPP-non-PDC) law. By generalization oftheprocedurebasedonP?olya’s theoremand techniques used for parameterdependentlinearmatrix inequality (PD-LMI) which have been studied previouslyin different contexts, ANS stability conditions with respect to thegeneral HPNQL function are obtained.

This paper considers output feedback robust model predictive control for the quasi-linear parametervarying (quasi-LPV) system with bounded disturbance. The so-called quasi-LPV means that the varyingparameters of the linear system are known at the current time, but unknown in the future. The controllaw is parameterized as a parameter-dependent dynamic output feedback, and the closed-loop stabilityis specified by the notion of quadratic boundedness. An iterative algorithm is proposed for the on-linesynthesis of the control law via convex optimization. A numerical example is given to illustrate theeffectiveness of the controller.

This paper improves some results in [Antonio Sala, Carlos Ari?o, Asymptotically necessary and sufficient conditions for stabilityand performance in fuzzy control: applications of Polya’s theorem, Fuzzy Sets and Systems 158 (2007) 2671-2686]. In the relaxationof the stability results, only a smaller number of artificial decision variables are required. Thus, we obtain the equivalent stabilityresults, with lower requirement on the computation.

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

We address the distributed model predictive control (MPC) for a set of linear local systems with decoupled dynamics and acoupled global cost function. By the decomposition of the global cost function, the distributed control problem is convertedto the MPC for each local system associated with a cost involving neighboring system states and inputs. For each localcontroller, the infinite horizon control moves are parameterized as N free control moves followed by a single state feedbacklaw. An interacting compatibility condition is derived, disassembled and incorporated into the design of each local control soas to achieve the stability of the global closed-loop system. Each local system exchanges with its neighbors the current statesand the previous optimal control strategies. The global closed-loop system is shown to be exponentially stable provided thatall the local optimizers are feasible at the initial time. Copyright