This article addresses the stabilisation of non-linear systems represented by a discrete-timeTakagi–Sugeno model. Based on an extended non-quadratic Lyapunov function and a nonparalleldistributed compensation (non-PDC) law, some additional slack matrices areintroduced. Compared with the existing methods, which collect the interactions among thesubsystems into a sequence of collection matrices, the new method re-collects the newlyintroduced slack matrices into another collection matrix. In this way, a stability result morerelaxed than some existing ones are obtained. Further, the convexity of the fuzzy blendingrules is utilised, with a further improved result obtained. The corresponding robust stabilityresults are also proposed. The effectiveness of the new results is validated by two simulationexamples.

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 paper addresses synthesis approaches to output feedback model predictive control(OFMPC) for systems with Hammerstein–Wiener nonlinearity and bounded disturbance/noise.The Hammerstein nonlinearity is removed (or partially removed) by constructing its inverse (orpseudo-inverse). The remaining nonlinearities in the model are incorporated by polytopic descriptions.At each sampling time, OFMPC finds a feedback gain and an estimator, such that the state ofthe closed-loop system asymptotically converges to a neighbourhood of the origin. A numericalexample is given to illustrate the effectiveness of the controller

This article addresses robust model predictive control (MPC) for systems with polytopicdescription. An existing off-line robust MPC enables the on-line computation as simple assearching a state feedback gain among the look-up table. We consider enlarging the region ofattraction of the off-line MPC by incorporating free perturbation items. First, a largerellipsoidal region of attraction is off-line constructed, in which a simple optimization problemis solved on-line. Then, outside of this larger ellipsoid, a standard robust MPC is solved onlinesuch that the overall region of attraction can be rendered as a much larger nonellipsoidalone. The proposed approach possesses all the merits of the off-line MPC and greatly enlargesthe region of attraction. A simulation example is given to demonstrate the effectiveness.