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This paper introduces an admissibilization condition for singular interval-valued fuzzy systems with a dynamic output-feedback controller using a linear matrix inequality approach. The derivation of the admissibility criterion (satisfying regularity, non-impulsiveness and stability) for the closed-loop system of the singular interval-valued fuzzy systems using the dynamic output-feedback controller is concerned. Here, the derived criterion is represented as the parameterized matrix inequalities depending on the membership functions of the system and the controller. To relax the derived parameterized matrix inequalities, this paper proposes a relaxation lemma based on the properties of the membership functions and their relations. By using this lemma, the parameterized matrix inequalities are converted into the matrix inequalities independent of the membership functions but not convex. Therefore, by introducing the structures of the variables and the congruent transformation matrix , a sufficient condition for the admissibility criterion is successfully given in terms of strict linear matrix inequalities. Two numerical examples are given to show the effectiveness of the proposed control.

This paper deals with an admissibilization problem of singular systems with uniform input quantization. The aim is to design a controller to guarantee the admissibility of the closed-loop system. To achieve this, this paper proposes a proportional-derivative state-feedback controller which includes non-linear control part to reject the effect of uniform input quantization. Based on the proposed controller, sufficient conditions are obtained in terms of linear matrix inequalities. Two examples show the feasibility of the proposed controller.

This paper deals with the problem of passivity analysis and passivity-based synthesis for continuous-time stochastic hybrid singular systems (SHSSs). First, a set of linear matrix inequalities for the stochastic admissibility and passivity, which is also known as the positive real lemma, is obtained for continuous-time SHSSs. The proposed condition successfully holds a necessary and sufficient condition for the positive realness of SHSSs, whereas the existing papers in the literature have been handled only sufficient conditions. Next, the passivity-based control synthesis problem is also considered based on the new positive real lemma. The passivity-based stabilization criterion for the closed-loop system with its mode-dependent state-feedback control is expressed in terms of matrix inequality. Thus, by introducing an additional slack matrix to the non-convex conditions, the feasible conditions for the control gain are obtained in terms of linear matrix inequalities. Finally, a numerical example is provided to show the effectiveness of the result.

This paper introduces a positive real lemma for continuous-time singular hybrid systems. The necessary and sufficient condition of stochastic admissibility and strict passivity for the singular hybrid systems is obtained in terms of linear matrix inequalities. The sufficient condition is derived by using mode-dependent Lyapunov function. In this step, two slack variables are inserted to make the proposed condition be necessary and sufficient condition in terms of strict linear matrix inequalities. Then, to prove the necessary condition, the positive real lemma for the hybrid system is proposed. Since the admissible singular system can be reformulated into stable normal system, the positive real lemma for the hybrid system holds. Thus, we give a necessary condition by constructing the solution of the proposed lemma from that of the hybrid systems.

In light of fuzzy weighting-dependent Lyapunov functions, a dynamic output-feedback control for singular T–S fuzzy systems is introduced. Based on a set-equivalence technique and fuzzy weighting-dependent Lyapunov functions, this paper derives a sufficient condition ensuring the singular T–S fuzzy systems to be admissible (regular, impulse-free and stable) in the form of strict parametric linear matrix inequalities (PLMIs). Then, for the closed-loop systems with a dynamic, rather than static, output-feedback controller, an admissibility criterion is given with strict PLMIs by specially representing the block entries of matrices in Lyapunov function. By appropriately choosing the structures of PLMI variables, the strict LMIs are obtained, where slack variables are included in the relaxation process fully exploiting the properties of the fuzzy weighting functions. Three numerical examples are provided to show the effectiveness of the introduced dynamic control.

This paper considers the problem of dynamic output-feedback stabilization for singular Markovian jump systems with partly unknown transition rates. First of all, for the augmented systems, the stabilization conditions are formulated in terms of non-convex matrix inequalities. For these conditions, this paper successfully derives new necessary and sufficient conditions in the form of linear matrix inequalities under partly unknown transition rates by using the variable elimination technique. Two numerical examples are provided to demonstrate the validity of the derived results.

The aim of this paper is to find the optimal mother wavelet function and wavelet decomposition level when denoising the Doppler cardiogram (DCG), the heart signal obtained by the Doppler radar sensor system. To select the best suited mother wavelet function and wavelet decomposition level, this paper presents the quantitative analysis results. Both the optimal mother wavelet and decomposition level are selected by evaluating signal-to-noise-ratio (SNR) efficiency of the denoised signals obtained by using the wavelet thresholding method. A total of 115 potential functions from six wavelet families were examined for the selection of the optimal mother wavelet function and 10 levels (1 to 10) were evaluated for the choice of the best decomposition level. According to the experimental results, the most efficient selections of the mother wavelet function are “db9” and “sym9” from Daubechies and Symlets families, and the most suitable decomposition level for the used signal is seven. As the evaluation criterion in this study rates the efficiency of the denoising process, it was found that a mother wavelet function longer than 22 is excessive. The experiment also revealed that the decomposition level can be predictable based on the frequency features of the DCG signal. The proposed selection of the mother wavelet function and the decomposition level could reduce noise effectively so as to improve the quality of the DCG signal in information field.

This paper proposes dynamic output-feedback networked control with actuator saturation and sensor failure for Markovian jump descriptor systems (MJDS). First, the mode-dependent dynamic output-feedback controller is described as a quasi-linear parameter varying system. Then, the stochastic admissibility criterion for the closed-loop system with sensor failure and actuator saturation is obtained as matrix inequalities. To obtain the feasible solution of the non-convex condition, this paper successfully obtains the equivalent condition in terms of strict linear matrix inequalities (LMIs) and the controller gains. A numerical example shows the validity of the proposed result.

This paper considers H ∞ filtering for continuous-time singular Markovian jump systems (SMJSs). While the existing researches in the literature suggested only sufficient conditions in terms of strict or non-strict linear matrix inequalities (LMIs) for sub-optimal H ∞ filtering, this paper successfully derives a necessary and sufficient condition in terms of strict LMIs for optimal H ∞ filtering. First, the necessary and sufficient condition that guarantees the stochastic admissibility of the filtering error system is obtained in terms of matrix inequalities. To reformulate it into strict LMIs, the congruence transformation by specially designed matrices is used. Two numerical examples show the validity of proposed H ∞ filtering.

This paper proposes a linear programming approach for stabilization of positive Markovian jump systems (PMJSs) with a saturated single input. The proposed approach first derives a sufficient condition for stabilization of PMJSs with input saturation based on the linear co-positive Lyapunov function. By introducing an intermediate scalar whose absolute value is less than the absolute value of product of nonnegative vector of the linear co-positive Lyapunov function and input matrix and constructing a special form of the controller gains, this approach obtains a modified condition applicable for the linear programming. Finally, four numerical examples show that the proposed approach gives the larger domain of attraction than the existing approach based on the quadratic Lyapunov function.

This paper considers the problem of dynamic output-feedback stabilization for singular Markovian jump systems with input saturation. The stabilization and set invariance conditions are first formulated in terms of non-convex matrix inequalities which is not linear matrix inequalities (LMIs). This paper, however, successfully derives the necessary and sufficient conditions for the non-convex inequalities in terms of LMIs. Also, an optimization problem is formulated to find the largest contractively invariant set in mean square sense of the closed-loop systems. Two numerical examples show the validity of the derived results.

This paper considers less conservative conditions of H ∞ control for Markovian jump fuzzy systems (MJFSs) with partly unknown transition rates and input saturation. To find H ∞ control for level γ, a set invariance condition and the stabilization conditions are first formulated in terms of parameterized linear matrix inequalities (PLMIs) by considering the properties of transition rates. Then, to derive the less conservative stabilization conditions, all possible slack variables are incorporated into the relaxation process with fully considering the property of the fuzzy weights. Two numerical examples are provided to illustrate the effectiveness of the proposed method.

In this study, a dynamic output-feedback stabilisation problem for Markovian jump systems (MJSs) with incomplete transition description and input quantisation is investigated. While the previous researches about output-feedback stabilisation for MJSs assumed that the transition rates are completely known, a more general situation where the transition rates are partly unknown is considered. Moreover, the proposed controller includes non-linear control part to eliminate the effect of input quantisation. Two numerical examples are provided to demonstrate the feasibility of the proposed dynamic output-feedback controller.

For the dynamic output-feedback stabilization of continuous-time singular Markovian jump systems, this paper introduces the necessary and sufficient condition , whereas the previous research works suggested the sufficient conditions. A special choice of the block entries of Lyapunov matrices leads to derive the necessary and sufficient condition in terms of linear matrix inequalities . A numerical example shows the validity of the derived results.

This paper proposes a method for designing an $$\mathcal {H}_\infty $$ state-feedback fuzzy controller for continuous-time Markovian jump fuzzy systems (MJFSs) with partly unknown transition rates. To find $$\mathcal {H}_\infty $$ control for level $$\gamma $$ , the stabilization conditions are first formulated in terms of parameterized linear matrix inequalities (PLMIs) for the MJFSs based on a fuzzy weighting-dependent Lyapunov function. Besides, to derive less conservative stabilization conditions, all possible slack variables are incorporated into the relaxation process with fully considering the property of the fuzzy weights. Finally, three examples are provided to verify the effectiveness of the proposed method.

This paper proposes a H state-feedback control for singular Markovian jump systems with incomplete knowledge of transition probabilities. Different from the previous results where the transition rates are completely known or the bounds of the unknown transition rates are given, a more general situation where the transition rates are partly unknown and the bounds of the unknown transition rates are also unknown is considered. Moreover, in contrast to the singular Markovian jump systems studied recently, the proposed method does not require any tuning parameters that arise when handling non-convex terms related to the mode-dependent Lyapunov matrices and the corresponding self-mode transition rates. Also, this paper uses all possible slack variables related to the transition rates into the relaxation process which contributes to reduce the conservatism. Finally, two numerical examples are provided to demonstrate the performance of H mode-dependent control.

This paper proposes the improved H ∞ state-feedback control for Markovian jump fuzzy systems (MJFSs) with incomplete knowledge of transition probabilities. From the fundamental first-order properties of the transition rates, two second-order properties are introduced without information on the lower and upper bounds of the transition rates, differently from other approaches in the literature. Based on these properties, this paper uses all possible slack variables into the relaxation process which contributes to reduce the conservatism. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method.

Summary This paper proposes less conservative stabilization conditions for Markovian jump systems with incomplete knowledge of transition probabilities and input saturation. The transition rates associated with the transition probabilities are expressed in terms of three properties, which do not require the lower and upper bounds of the transition rates, differently from other approaches in the literature. The resulting conditions are converted into the second-order matrix polynomial of the unknown transition rates. The polynomial can be represented as quadratic form of vectorized identity matrices scaled by one and the unknown transition rates. And then, the LMI conditions are obtained from the quadratic form. Also, an optimization problem is formulated to find the largest estimate of the domain of attraction in mean square sense of the closed-loop systems. Finally, two numerical examples are provided to illustrate the effectiveness of the derived stabilization conditions. Copyright © 2016 John Wiley & Sons, Ltd.

This paper proposes a state-feedback controller design for linear parameter-varying systems with interval uncertain parameters that are interval-type uncertain weight functions for convex combinations of linear subsystems. The proposed controller hires secondary convex parameters generated through the lower and upper boundaries of the interval uncertain parameters. The resulting stabilization condition is expressed in terms of parameterized linear matrix inequalities, which are then converted into linear matrix inequalities using a parameter relaxation technique. The simulation results illustrate the robustness of the proposed controller.

This paper introduces the stabilization condition for the Markovian jump systems (MJSs) with incomplete knowledge of transition probabilities and input quantization. To obtain the less conservative stabilization condition, an appropriate weighting method is proposed by using all possible slack variables from the relationship of the transition probabilities, which does lead to a form of linear matrix inequalities (LMIs). Further, a proposed controller not only stabilizes the MJS with incomplete knowledge of transition probabilities but also eliminates the effect of input quantization. Simulation examples report the effectiveness of the proposed criterion.

This paper introduces an improved stability criterion for discrete-time Lur'e systems with sector- and slope-restrictions. For the stability criterion, a Lur'e Lyapunov functional candidate is constructed to include quadratic terms and integration terms with nonlinearities. To handle the resulting integration terms in the Lyapunov difference, there is proposed a new bound lemma where the integration terms are relaxed into the second-order terms by the geometric point of view. In addition, an appropriate weighting method uses slack variables from the sector- and slope-restrictions. In the overall derivation, the stabilization condition is formulated in terms of a parameterized linear matrix inequality (PLMI), which is then converted into the linear matrix inequality. An example illustrates that the proposed criterion presents a less conservative result than the previous criteria in the literature.

This paper proposes a linear programming (LP) approach for stabilization of positive Markovian jump systems (PMJSs) with input saturation. First of all, we derive the sufficient conditions for stabilization of PMJSs with input saturation based on the linear co-positive Lyapunov function. However, since the decision variables in the obtained conditions are mutually coupled, the conditions are not linear. Therefore, to obtain the condition that can be solved by the LP, we propose the methods to properly choose the decision variables. Furthermore, we give a process to acquire the largest domain of attraction. Finally, we suggest two numerical examples to illustrate the validity of the proposed methods.

This paper improves a stabilization condition of one-step receding horizon control for discrete-time linear systems with model uncertainties. By using matrix inversion lemma, the improved stabilization condition is derived in terms of a matrix inequality associated with the terminal-time weighting matrix of the cost. A numerical example verifies that the proposed condition guarantees the larger maximum allowable uncertainty bound than the existing condition in the literature.

This paper suggests H ∞ filtering for singular Markovian jump systems (SMJSs) with partly unknown transition rates. While the existing researches in the literature have derived only the sufficient conditions, this paper successfully demonstrates the necessary and sufficient condition for the existence of H ∞ filtering for SMJSs with partly unknown transition rates. First, a new bounded real lemma for SMJS is derived in terms. Next, the matrix inequalities which come from the bounded real lemma for the filtering error system with partly unknown transition rates are reformulated into the strict LMIs. Two numerical examples are presented to show the effectiveness of the proposed result.

In this paper, the H 2 control for discrete-time Markovian jump fuzzy system (MJFS) with partly known transition probabilities is considered. To deal with unknown transition probabilities, convex property of the normalized unknown transition probabilities and lower bound lemma for the inversion of the matrix summation are used. Then, using the properties of fuzzy weights, quadratic condition of stochastic stability and guaranteed cost is obtained. Finally, linear matrix inequalities (LMIs) are derived from the quadratic condition. In order to illustrate the effectiveness of the proposed theorem, the practical problem is given as a numerical example.

In this paper, the stabilization problem for continuous-time singular Markovian jump systems with unmeasurable states is investigated. Differently from the previous researches, the dynamic output-feedback stabilization conditions are formulated in terms of strict linear matrix inequalities by using variable elimination lemma and new partitioning method about mode-dependent Lyapunov matrices. Numerical examples are provided to demonstrate the validity of the derived results.

In this paper, we propose a moving object detection algorithm that enables to detect moving objects with collision risk in rear of the vehicle by using image sequences from a vehicle-mounted monocular rear-view fisheye camera.

This paper considers improved ℋ ∞ state-feedback control for discrete-time Markovian jump systems with incomplete knowledge of transition probabilities. To achieve the better ℋ ∞ performance, this paper proposes two valuable approaches. First, under the assumption that the lower and upper bounds of unknown transition probabilities are known, the closed-loop stabilization conditions are represented as convex combination with these bounds. Second, a new lower bound lemma for the inversion of the matrix summation is investigated. This lemma enables the inversion of the matrix summation to be replaced by free variable which does not contain the transition probabilities. Thus, the ℋ ∞ stabilization conditions consist of two parts which are transition probability independent part and dependent part. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method.

This paper considers the ℋ ∞ state-feedback control for continuous-time Markovian jump systems with partly unknown transition probabilities. The aim of this paper is to derive the ℋ ∞ stabilization condition such that the MJS with partly unknown transition probabilities is stochastically stable with γ-disturbance attenuation. First of all, the transition rates associated with the transition probabilities are expressed in terms of the three properties without the lower and upper bounds of the transition rates, differently from other approaches in the literature. Then, with consideration of the properties of transition rates, the ℋ ∞ stabilization conditions are derived in the quadratic form. And then the quadratic form can be replaced by the linear matrix inequalities(LMIs). Finally, a numerical example is presented to illustrate the effectiveness of the proposed method.

This paper proposes vision based mura detection algorithm for the black resin-coated steel by using property of line scan camera. The proposed algorithm consists of three parts: preprocessing, selection of threshold value, and finally binarization and post processing. Preprocessing consists of moving average filtering, image partitioning and additional weight for black defects. Second, to distinguish between defect and background we must choose proper threshold value. Finally, we binarize original image by using threshold value and use the image opening and closing to eliminate small noise. The simulation results show detection accuracy of the proposed algorithm.

This paper proposes a bias-compensated affine projection algorithm (BC-APA) to eliminate bias due to noisy input data and to reduce the performance degradation due to highly correlated input data. A new affine projection algorithm (new APA) using innovative input data is presented for highly correlated input data. We analyze the bias in this innovative new APA under noisy input data and remove it. To remove the bias, an estimation method for the input noise variance is presented and explained. In simulations, the BC-APA provided both fast convergence rate and small mean square deviation. Based on improved precision to estimate a finite impulse response of an unknown system, the BC-APA can be applied extensively in adaptive signal processing areas.

This paper proposes mura region detection algorithm by using two-dimensional fast Fourier transform (2D FFT) with exponential kernel for black resin-coated steel. If the mura exists in the black resin-coated steel image, the image has large low-frequency component. To improve accuracy, multiply exponential kernel to low frequency region. The simulation results show improved performance.