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The robust exponential stabilization for a class of the uncertain switched neutral nonlinear systems with time‐varying delays based on the sampled‐data control is investigated in this paper. The closed‐loop system with sampled‐data control is modeled as a continuous time system with a time‐varying piecewise continuous control input delay. Considering the relationship between the sampling period and the dwell time of two switching instants, sampling interval with no switching and sampling interval with one switching are discussed, respectively. By Wirtinger‐based inequality, Wirtinger‐based double integral inequality, and free‐weighting matrix technique, some delay‐dependent sufficient conditions are given to guarantee the exponential stability of uncertain switched neutral nonlinear systems under asynchronous switching. In addition, sampled‐data controllers can also be designed by special operations of matrices. Finally, two numerical examples are used to show the effectiveness of the approach proposed in this paper. [ABSTRACT FROM AUTHOR]

This paper investigates geometrically (Q,S,R)‐incremental dissipativity and incremental stability for switched time‐varying nonlinear discrete‐time systems. A geometrically (Q,S,R)‐incremental dissipativity concept is proposed for switched nonlinear discrete‐time systems by using multiple storage functions and multiple incremental supply rate. Furthermore, the sufficient conditions of geometrically (Q,S,R)‐incremental dissipativity are given under the design of state‐dependent switching law. The incremental stability conditions are derived for geometrically (Q,S,R)‐incrementally dissipative switched systems. By designing of a composite state‐dependent switching law, the feedback interconnected switched systems are ensured to be geometrically (Q,S,R)‐incrementally dissipative. A numerical example is given to illustrate the validity of the proposed approach. [ABSTRACT FROM AUTHOR]

Abstract: This paper studies the problems of L1‐gain analysis and control for switched positive systems with dwell time constraint. The state‐dependent switching satisfies a minimal dwell time constraint to avoid possible arbitrary fast switching. By constructing multiple linear co‐positive Lyapunov functions, sufficient conditions of stability and L1‐gain property are derived under the proposed switching strategy. Then, an effective state feedback controller is designed to ensure the positivity and L1‐gain property of the closed‐loop system. Finally, a simulation example is given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the incremental H ∞ control for switched nonlinear systems by using a state-dependent switching law and an average dwell time approach incorporated with multiple Lyapunov functions. Even if all subsystems are unstable, a sufficient condition for the incremental H ∞ control problem to be solvable is derived based on the design state-dependent switching law. Furthermore, when all subsystems are incrementally globally asymptotically stable (IGAS), the switched nonlinear system under the average dwell time scheme is IGAS and possesses a weighted incremental L 2 -gain. Then, we extend this result to the case where both IGAS subsystems and unstable subsystems coexist, if the activation time ratio between IGAS subsystems and unstable ones is not less than a specified constant, sufficient conditions for the weighted incremental H ∞ performance of the switched system are guaranteed. Two numerical examples are given to illustrate the validity of the proposed approach. [ABSTRACT FROM AUTHOR]

Exponentially incremental (Q,S,R)-dissipativityand incremental stability for switched time-varying nonlinear systems are studied whose subsystems are not required to be exponentially incrementally (Q,S,R)-dissipative. The sufficient conditions for switched time-varying nonlinear systems to be exponentially incrementally (Q,S,R)-dissipative are presented by the design of state-dependent switching laws. Incremental stability for switched time-varying nonlinear systems are derived based on exponentially incremental (Q,S,R)-dissipativity. Exponentially incremental (Q,S,R)-dissipativity is shown to be preserved under feedback interconnection by the design of a composite state-dependent switching law. Two simulation examples are provided to show the effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates control for general 2D nonlinear systems based on a 2D Takagi–Sugeno (T–S) fuzzy model. The system under consideration is an extension of the general 2D linear system to a nonlinear case. Taking the spatial and structural features into consideration, a 2D T–S fuzzy model is first established. In designing the controller, the inputs are regarded as variables independent from the states and then basis-dependent free matrices are introduced. It has been shown that separation of the input and state variables does not lead to any conservativeness compared with the commonly used method. Thus, a fuzzy controller is designed using a common free matrix, resulting in only r linear matrix inequalities. The computational advantage is obvious for fuzzy systems with a large number of fuzzy rules. We also demonstrate that the proposed method is less computationally expensive than the approach in which the input variable, state variable and its forward-stepping state are all separately considered, although these two methods can achieve the same optimal performance. Simulation examples are used to demonstrate the technique and its advantages. [Copyright &y& Elsevier]

This article is concerned with stability analysis and stabilisation problems for a class of two-dimensional (2-D) nonlinear discrete systems. First, the stability condition is derived for 2-D systems with nonlinearity by exploiting the Lyapunov method. Based on this result, a state feedback controller and an output feedback controller are designed to achieve stability for the closed-loop system. Next, H∞ controllers are given in terms of the linear matrix inequality (LMI). Finally, some numerical examples are used to illustrate the effectiveness of the results. [ABSTRACT FROM AUTHOR]