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 investigates the parameter-dependent open-loop model predictivecontrol (PDOLMPC) scheme for systems with a polytopic uncertaintydescription. PDOLMPC parameterizes the infinite horizon control moves intoa number of free control moves followed by a single state feedback law.The free control moves (excluding the first one) are parameter dependentand constructed upon all of the extreme realizations of the uncertainty beforethe switching horizon N. Our primary contribution is to point out that thisPDOLMPC is a relaxed version of the feedback MPC. Thus, some propertiesof nominal MPC, such as enhancement of optimality and enlargement ofregion of attraction by increasing the switching horizon, can be inherited inPDOLMPC. These properties are theoretically important for robust MPC anda simulation example is given for demonstration.

This paper studies poly-quadratic stability of nonlinear systems representedby a Takagi-Sugeno (T-S) discrete fuzzy model. A system is polyquadraticallystable when its stability can be verified by a parameter dependentLyapunov function. There are already some results in this area. This paper,however, presents less conservative results by adopting more slack-matrixvariablesin the linear matrix inequalities (LMIs). The parallel distributedcompensation (PDC) law is utilized in both the analysis and the synthesisproblems. The effectiveness of the new results in this paper is validated by asimulation example.

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.