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This paper addresses the nonfragile sensor fault estimation problem for a class of two-dimensional (2-D) nonlinear systems. The underlying system is described by the well-known Fornasini–Marchesini model. The system parameters are subject to abrupt changes regulated by the Markovian process for which the entries of the mode transition probability matrix are partially accessible. A novel 2-D nonfragile state estimator is constructed to achieve the sensor fault estimation where the estimator gains are allowed to be randomly perturbed. Then, together with the Lyapunov stability theory, the stochastic analysis techniques are employed to derive the sufficient conditions that guarantee the following three performance requirements: 1) the exponential stability of the estimation error dynamics; 2) the prespecified constraint on the energy-to-peak gain; and 3) the prespecified restriction on the prescribed power bound. Moreover, the estimator gains are parameterized by using the convex optimization method. Finally, a numerical example is provided to illustrate the effectiveness of the addressed estimation algorithm. [ABSTRACT FROM AUTHOR]

This paper is concerned with the robust H{\infty } fault detection problem for a class of uncertain discrete-time nonlinear 2-D systems subject to Round-Robin scheduling protocol. The Takagi–Sugeno fuzzy model is used to approximate the nonlinearities, where the linear fractional uncertainties enter the system in a random way. A kind of widely used communication mechanism, namely, Round-Robin communication protocol, is adopted to periodically schedule the sensors and the fault detectors to realize the information exchange in order to reduce the bandwidth usage in a networked environment with limit resource. An improved 2-D fuzzy residual generator is constructed to detect the possible fault, where the stability analysis of the resulting augmented 2-D system is discussed. It is accomplished by using a combination of the basis-dependent Lyapunov-like function and the stochastic analysis techniques. Sufficient conditions are first established to guarantee the globally asymptotic stability of the error dynamics of the state estimation with prescribed H{\infty } performance constraints. Then, a residual generator is proposed to detect the possible faults. The effectiveness of the developed algorithm is demonstrated via application to the fault detection problem for a thermal process. [ABSTRACT FROM AUTHOR]

This paper is concerned with the robust \mathscr H\infty filtering problem for a class of 2-D uncertain fuzzy systems with randomly occurring mixed delays (ROMDs). The underlying 2-D systems are described by the Fornasini–Marchesini model, and the uncertainty is expressed in a linear fraction form. An improved Takagi–Sugeno (T–S) fuzzy model corresponding to the spatial promise variables is adopted to represent the complicated 2-D nonlinear system. The mixed delays consisting of both discrete and distributed delays are allowed to appear in a random manner governed by two sets of Bernoulli distributed white sequences with known probability. A full-order fuzzy filter is constructed to estimate the output signal such that, in the presence of parameter uncertainties and ROMDs, the dynamics of the estimation errors is asymptotically stable with a prescribed \mathscr H\infty disturbance attenuation level. Based on the stochastic analysis technique and the Lyapunov-like functional, sufficient conditions are established to ensure the existence of the desired filters, and the explicit expressions of such filters are derived by means of the solution to a class of convex optimization problems that can be solved via standard software packages. A numerical example is provided to demonstrate the effectiveness of the developed filter design algorithms, and the filter performances with and without fuzzy rules are also compared. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the H\infty control problem for a class of 2-D Takagi–Sugeno fuzzy described by the second Fornasini–Machesini local state-space model with time-delays and missing measurements. The state delays are allowed to be time-varying within a known interval. The measurement output is subject to randomly intermittent packet dropouts governed by a random sequence satisfying the Bernoulli distribution. The purpose of the addressed problem is to design an output-feedback controller such that the closed-loop system is globally asymptotically stable in the mean square and the prescribed H_\infty performance index is satisfied. By employing a combination of the intensive stochastic analysis and the free weighting matrix method, several delay-range-dependent sufficient conditions are presented that guarantee the existence of the desired controllers for all possible time-delays and missing measurements. The explicit expressions of such controllers are derived by means of the solution to a class of convex optimization problems that can be solved via standard software packages. Finally, a numerical simulation example is given to demonstrate the applicability of the proposed control scheme. [ABSTRACT FROM PUBLISHER]

In this note, we consider a novel reliable estimation problem for a class of two-dimensional (2-D) discrete linear systems with incomplete observations. The time delays existing in 2-D systems are assumed to be infinitely distributed in the discrete-time domain. Factors leading to incomplete observations include delayed and missing measurements, sensor quantization and saturations. A uniform mathematical model is employed to describe the phenomenon of incomplete observations. Our attention is focused on the design of a linear state estimator for the discussed 2-D systems, such that for all admissible sensor failures, possible infinite distributed time delays and incomplete observations, the error dynamics is mean-square asymptotically stable, and the steady-state error of the estimation is not more than a prescribed level. The flexibility of the proposed approach is confirmed by a numerical simulation. [ABSTRACT FROM AUTHOR]

Objective: To assess the therapeutic effect of hyaluronate acid (HA) injection through the subpatellar route for treatment of chondromalacia patellae (CP)., Methods: Eighty-eight patients with the diagnosis of CP were enrolled in this prospective study, including 38 with early CP (CP group) and 50 with advanced CP (patellofemoral arthritis group) diagnosed based on image presentations. All the patients received intra-articular HA injections through a subpatellar route once a week for 5 consecutive weeks. The primary outcome measures included WOMAC index scores and Lequesne scores before and at 4, 12, 26 and 52 weeks after the injections. The secondary outcome measures included the 30-m walking time and stair ascending and descending time (one floor) before and at 1, 2, 3, and 4 weeks after the injections., Results: In both groups the patients showed significantly decreased WOMAC scores and Lequesne scores at 4, 12, 26 and 52 weeks after HA injections as compared with the baseline scores (all P < 0.01). No significant difference was found between the two groups in WOMAC scores and Lequesne scores at 4 or 12 weeks after the injections (both P >0.05). The WOMAC scores and Lequesne scores at 26 and 52 weeks after the injections were significantly higher in patellofemoral arthritis group than in CP group (both P < 0.05). In both groups, the 30-m walking time and the stair ascending and descending time decreased significantly at 1, 2, 3, and 4 weeks after HA injections (all P < 0.05) without significant differences between the two groups (all P >0.05)., Conclusions: HA injection through the subpatellar route is effective for treatment of CP. HA injection produces better long-term efficacy for treatment of early CP than for advanced CP where patellofemoral arthritis occurs.