This paper investigates the stochastic stability of the continuous-discrete maximum correntropy cubature Kalman filter (CD-MCCKF), which is developed by embedding the maximum correntropy criterion as an optimization strategy into the continuous-discrete filtering architecture. By assuming that the relevant functions satisfy certain properties, we first establish the convergence of the employed numerical method and fixed-point iteration technique. Subsequently, combined with the findings on the error covariance boundary, it is proved that the estimation error of CD-MCCKF keeps mean-square bounded under specific conditions. To validate this stability analysis finding and evaluate the filtering performance, we conduct a classical case study. Simulation results confirm that CD-MCCKF not only maintains bounded estimation errors, but also surpasses the conventional continuous-discrete filters in terms of accuracy and convergence.

The affine projection sign algorithm (APSA) has garnered significant attention in adaptive filtering due to its exceptional robustness and reduced computational demands. Nevertheless, the inherent use of a fixed projection order in APSA can compromise filtering accuracy and convergence speed. To address this issue, we introduce an innovative strategy for dynamically updating the projection order, resulting in an enhanced version of APSA called the evolving order based APSA (E-APSA). This evolving strategy compares the instantaneous power of output error to a threshold determined by the steady-state mean-square error of APSA, thereby enabling variable projection orders. Furthermore, we provide computational complexity and convergence analyses for E-APSA. Simulation results demonstrate that, compared to other related algorithms, E-APSA offers a significantly faster convergence rate while maintaining competitive steady-state misalignment.

In this paper, jointly with the exponential weighted generalized maximum correntropy (GMC) criterion and the linear constraint framework, we derive a recursive constrained adaptive filtering algorithm named recursive constrained GMC with forgetting factor (FF-RCGMC). In addition, due to a lack of constraint information during the learning process, FF-RCGMC will diverge or even fail to work after some iterations. Therefore, we propose a more stable version by introducing a constraint-forcing strategy into FF-RCGMC and call this robust type as constraint-forcing FF-RCGMC (CFFF-RCGMC). Some simulation results in system identification under non-Gaussian noisy environments validate the effectiveness of CFFF-RCGMC.

In robust adaptive filtering, the affine projection sign algorithm (APSA) is widely used in practice due to the desirable convergence behavior and low computational cost. Several variants of APSA have been derived from the variable step-size method and the combination strategy. For APSA, to further improve the filtering performance, this paper proposes a new filtering performance-enhanced (APSA) by optimizing a weighted cost function. Specifically, motivated by individual-weighting factors, our proposed algorithm, i.e., IWF-APSA, uses an individual-weighting factor to a corresponding input signal, while it has similar computational complexity to APSA. We also conduct the mean-square convergence analysis of IWF-APSA. The simulation results show that IWF-APSA achieves a better filtering performance in terms of convergence rate and filtering accuracy in system identification.

In this article, the stability issues are addressed for switched linear systems (SLSs) with mode-dependent average dwell time (MDADT). By dividing the dwell time into several segments, and constructing a reverse timer which starts timing at the end of each segment, we propose a new reverse-timer-dependent multiple discontinuous Lyapunov function (RTDMDLF), which is more general than the multiple Lyapunov function (MLF) and the multiple discontinuous Lyapunov function (MDLF). With the help of the RTDMDLF approach, several convex and nonconvex stability conditions are derived for SLSs with both stable and unstable subsystems, and the relation of these conditions and existing ones is revealed. Moreover, the stability conditions for SLSs with all stable subsystems are also given. All the results are presented in terms of infinite-dimensional linear matrix inequalities (LMIs), which can be relaxed into computable conditions by using a discretized approach. It is shown that the tighter bound of MDADT can be achieved by the RTDMDLF approach compared with those of the literature. Finally, the advantages of the results are illustrated within three numerical examples.

In this letter, an accurate Gaussian sum-smoothing approach is derived for the continuous-discrete systems, where the dynamics can be modeled with nonlinear Itô-type stochastic differential equations and the measurements are obtained at discrete sampling times with non-Gaussian noise. The proposed smoothing method is derived by applying a bank of parallel accurate continuous-discrete extended-cubature Kalman filters used in the classical Gaussian state estimation to approximate the nonGaussian estimation densities as a finite number of weighted sums of Gaussian densities. The performances of the proposed method are compared with the recently presented filters based on the maximum correntropy criterion in a simulated application and the numerical results show that the new approach is more accurate and robust than others.

In this letter, a novel kernel adaptive algorithm, called kernel recursive generalized maximum correntropy algorithm (KRGMC), is derived in a kernel space and under the generalized maximum correntropy (GMC) criterion. The proposed kernel algorithm can effectively scale down the dynamic recursive weight coefficients influenced by the impulsive estimate error to avoid the significant performance degradation. The superior performance of the proposed algorithm is verified by numerical simulations about short-time series prediction in alpha-stable noise environment.

This paper investigates the finite-time exponential stability analysis and stabilization problem of discrete-time switched nonlinear systems without stable subsystems. In the stability analysis, the Takagi-Sugeno (T-S) fuzzy model is employed to approximate nonlinear subsystems. With two level functions, namely, crisp switching functions and local fuzzy weighting functions, we introduce switched fuzzy systems with approximation errors, which inherently contain both the features of the switched systems and T-S fuzzy systems. By constructing the “decreasing-jump” piecewise Lyapunov-like functions and minimum dwell time technique, a finite-time exponential stability of switched fuzzy systems with bounded approximation errors is obtained. Then, based on the finite-time exponential stability, a multiobjective evolution algorithm (nondominated sorting genetic algorithm, NSGA-II), which considers two conflicting objectives, such as the average convergence error and the average switching cost, is proposed to generate tradeoff switching sequences to stabilize the discrete-time switched nonlinear systems over a finite-time interval. A numerical example and a practical example are provided to illustrate the effectiveness of the stability and the algorithm, respectively.

In this paper, we investigate the problem of exponential stability and asynchronous stabilization for a class of switched nonlinear systems. The Takagi and Sugeno (T-S) fuzzy model is employed to approximate the subnonlinear dynamic systems. With two-level functions, namely, crisp switching functions and local fuzzy weighting functions, we introduce continuous-time switched fuzzy systems, which inherently contain the features of the switched hybrid systems and T-S fuzzy systems. By the use of delicately constructed piecewise Lyapunov-like functions (PLFs) and minimum dwell time method, we obtain the exponential stability of the switched fuzzy systems, which allows us to have stable and unstable nonlinear subsystems. In practice, for the control problem, it inevitably takes some time to identify the system modes and apply the matched controller, the asynchronous phenomena between the system modes switching and the controllers switching generally exists. Based on the result of stability, the fuzzy state feedback controller under asynchronous switching is proposed for switched fuzzy systems. In addition, the lower bound of minimum dwell time can be obtained using convex optimization such that the switched fuzzy system can be exponentially stabilized if its minimum dwell time is larger than the bound. The stability results and control laws of the switched fuzzy systems are formulated in the form of linear matrix inequalities that are numerically feasible. Finally, two illustrated numerical examples are presented to show the effectiveness of the obtained theoretical results.

This paper is concerned with the problem of delay-dependent H∞filter design for a class of discrete-time nonlinear interconnected system with time-varying delays via the Takagi-Sugeno (T-S) fuzzy model. The T-S fuzzy model consists ofNtime-delay T-S fuzzy subsystems, and a decentralized H∞filter is designed for each subsystem. Based on the delay-dependent piecewise Lyapunov-Krasovskii functional (DDPLKF) and with an improved free-weighting matrix technique, the delay-dependent stability and a prescribed H∞performance index are guaranteed for the overall filtering error system. A sufficient condition for the existence of such a filter is established by using linear matrix inequalities (LMIs) that are numerically feasible. Two numerical examples are given to demonstrate the effectiveness and advantage of the proposed approach.

In general, due to the interaction among subsystems, it is difficult to design an Hinfinity filter for nonlinear interconnected systems. This paper introduces a decentralized Hinfinity fuzzy filter design for nonlinear interconnected systems with multiple time delays via T-S fuzzy models. The T-S fuzzy model consists of N time-delay T-S fuzzy subsystems. The decentralized Hinfinity filter is designed based on this model, which the asymptotic stability and a prescribed Hinfinity performance index are guaranteed for the overall filtering error system. A sufficient condition for the existence of such a filter is established by using linear matrix inequalities that are numerically feasible. A simulation example is given to show the effectiveness of this approach.

This paper describes a decentralizedHinfinfilter design for discrete-time interconnected fuzzy systems based on piecewise-quadratic Lyapunov functions. The systems consist ofJdiscrete-time interconnected Takagi-Sugeno (T-S) fuzzy subsystems, and a decentralizedHinfinfilter is designed for each subsystem. It is shown that the stability of the overall filtering-error system withHinfinperformance can be established if a piecewise-quadratic Lyapunov function can be constructed. Moreover, the parameters of filters can be obtained by solving a set of linear matrix inequalities that are numerically feasible. Two simulation examples are given to show the effectiveness of the proposed approach.

This paper considers the robustHinfincontrol of uncertain discrete-time fuzzy systems with time delays based on piecewise Lyapunov--Krasovskii functionals. It is shown that the stability withHinfindisturbance attenuation performance can be established for the closed-loop fuzzy control systems if there exists a piecewise Lyapunov--Krasovskii functional, and moreover, the functional and the corresponding controller can be obtained by solving a set of linear matrix inequalities that are numerically feasible. A numerical example is given to demonstrate the efficiency and the advantage of the proposed method.

This paper is concerned with stability analysis and H(infinity) decentralized control of discrete-time fuzzy large-scale systems based on piecewise Lyapunov functions. The fuzzy large-scale systems consist of J interconnected discrete-time Takagi-Sugeno (T-S) fuzzy subsystems, and the stability analysis is based on Lyapunov functions that are piecewise quadratic. It is shown that the stability of the discrete-time fuzzy large-scale systems can be established if a piecewise quadratic Lyapunov function can be constructed, and moreover, the function can be obtained by solving a set of linear matrix inequalities (LMIs) that are numerically feasible. The H(infinity) controllers are also designed by solving a set of LMIs based on these powerful piecewise quadratic Lyapunov functions. It is demonstrated via numerical examples that the stability and controller synthesis results based on the piecewise quadratic Lyapunov functions are less conservative than those based on the common quadratic Lyapunov functions.

This paper presents a novel approach to stability analysis of a fuzzy large-scale system in which the system is composed of a number of Takagi-Sugeno (T-S) fuzzy subsystems with interconnections. The stability analysis is based on Lyapunov functions that are continuous and piecewise quadratic. It is shown that the stability of the fuzzy large-scale systems can be established if a piecewise Lyapunov function can be constructed, and, moreover, the function can be obtained by solving a set of linear matrix inequalities (LMIs) that are numerically feasible. It is also demonstrated via a numerical example that the stability result based on the piecewise quadratic Lyapunov functions is less conservative than that based on the common quadratic Lyapunov functions. The H infinity controllers can also be designed by solving a set of LMIs based on these powerful piecewise quadratic Lyapunov functions.