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