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This paper presents two novel general summation inequalities, respectively, in the upper and lower discrete regions. Thanks to the orthogonal polynomials defined in different inner spaces, various concrete single/multiple summation inequalities are obtained from the two general summation inequalities, which include almost all of the existing summation inequalities, e.g., the Jensen, the Wirtinger-based and the auxiliary function-based summation inequalities. Based on the new summation inequalities, a less conservative stability condition is derived for discrete-time systems with time-varying delay. Numerical examples are given to show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper considers the problem of unified mode-dependent and mode-independent filters design for continuous-time singular systems with Markovian jumping parameters and time-varying delays. The main objective of this paper is to design the L 2 − L ∞ , H ∞ , passivity, strict ( Q , S , R )-dissipativity, very-strict passivity filters in a unified framework so as to ensure that the filter error system is stochastically admissible and extended dissipative. By tuning the weighting matrices, the extended dissipativity performance can reduce to the L 2 − L ∞ performance, H ∞ performance, passivity, strict ( Q , S , R )-dissipativity and very-strict passivity, respectively. A mode-dependent and delay-dependent stochastic Lyapunov–Krasovskii functional is proposed to reflect the information of Markovian jump modes and the time-varying delays, and a set of linear matrix inequalities (LMIs) are utilized to derive sufficient conditions which guarantee that the desired unified filters can be constructed. Three numerical examples including an oil catalytic cracking process (OCCP) are employed to verify the usefulness and effectiveness of the main results obtained. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of stability analysis for continuous-time Takagi–Sugeno (T–S) fuzzy systems. A new series of line-integral Lyapunov functions (LILFs) is developed which can be seen as an extension of the existing LILF. Without the difficulty of dealing with the time derivatives of the membership functions, relaxed stability conditions are derived by combining the matrix Polya׳s theorem in terms of linear matrix inequalities. To further illustrate the effectiveness of the extended LILFs, the T–S fuzzy systems with time delay are also studied and corresponding relaxed stability conditions are obtained as well. Finally, several numerical examples are provided to illustrate the improvement of the proposed results. [ABSTRACT FROM AUTHOR]

This paper deals with the problems of stability and stabilization for continuous-time Takagi–Sugeno (T–S) models. By employing the order relation information of the membership functions (MFs), the transformation matrix and the pseudo-MF vector are obtained. The conventional continuous-time T–S fuzzy model is then transformed to a new compact T–S model, based on which relaxed stability and stabilization conditions are derived in the form of linear matrix inequalities. An improved approach to constructing the transformation matrix is presented, which could take full advantage of the order relation information of the MFs and further reduce the conservatism. Numerical examples are provided to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper aims to study a class of Markovian switching random systems with stochastic processes whose α -order moments ( α > 1 ) are finite. Compared with the existing results, the existence and uniqueness of solutions to random systems with Markovian switching is not given as a priori information but guaranteed under some general conditions. The corresponding criteria on noise-to-state stability and boundedness are presented by employing the Lyapunov method. Finally, based on the derived results, a design procedure of state-feedback tracking control is proposed, which is illustrated through two examples. [ABSTRACT FROM AUTHOR]

This paper is concerned with the stability and stabilization problem for discrete-time Takagi–Sugeno (T–S) fuzzy systems. By taking into account the order relation information of membership functions (MFs), a so-called pseudo-MF vector is obtained through the transformation matrix; an improved approach to constructing the transformation matrix is given in order to make the best of the information of the MFs. Based on the transformed T–S fuzzy systems, relaxed stability and stabilization conditions are derived via both quadratic and non-quadratic Lyapunov functions. Numerical examples are provided to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, the problem of global state regulation by output feedback is considered for a class of uncertain feedforward nonlinear systems with free-delay or time-delay states. Compared with existing results, we construct a novel observer-based controller with gain exponent to achieve the global state regulation via single output feedback under less conservative assumptions. Further, by using the Lyapunov–Krasovskii theorem, we show that the control scheme proposed is available to a class of time-delay systems with input and output dependent incremental rate. Finally, a numerical example is given to illustrate the usefulness of our results. [ABSTRACT FROM AUTHOR]

This paper studies the problem of decentralized stabilization for a class of large-scale stochastic high-order time-delay feedforward nonlinear systems. A series of delay-independent state feedback controllers is constructed, which is based on the approach of adding one power integrator. The stochastically global asymptotic stability (GAS) of the closed-loop system under the above-mentioned controllers is proved by Lyapunov–Krasovskii theorem and homogeneous domination approach. A simulation example is given to illustrate the effectiveness of the results of this paper. [ABSTRACT FROM AUTHOR]

This paper addresses the finite-time dynamic coverage problem for mobile sensor networks in unknown environments. By introducing a condition where dynamic coverage of all points within the sensing range of each sensor exceeds the desired coverage level by a positive constant, a switching control strategy is developed to guarantee the achievement of desired coverage of the whole mission domain in finite time. The environment is modeled by a density function and neural networks are introduced to learn the function. Due to the approximation capability of neural networks, the proposed control scheme can learn the environment without a priori knowledge on the structure of the density function. [ABSTRACT FROM AUTHOR]