Piecewise Analysis Research Articles

New results on H ∞ filter design for nonlinear systems with time-delay through a T-S fuzzy model approach

H ∞ filter design for nonlinear systems with time-delay via a T-S fuzzy model approach is investigated based on a piecewise analysis method. Two cases of time-varying delays are fully considered: one is the time-varying delay being continuous uniformly bounded while the other is the time-varying delay being differentiable uniformly bounded with delay-derivative bounded by a constant. Based on a piecewise analysis method, the variation interval of the time delay is first divided into several subintervals, then the convexity property of the matrix inequality and the free weighting matrix method are fully used in this article. Some novel delay-dependent H ∞ filtering criteria are expressed as a set of linear matrix inequalities, which can lead to much less conservative analysis results. Finally, a numerical example is given to illustrate that the results in this article are more effective and less conservative than some existing ones.

Delay-dependent stability criteria for systems with asymmetric bounds on delay derivative

This paper discretizes the states, a method introduced in [18] for constant delayed systems, not only in constructing the Lyapunov–Krasovskii (L–K) functional but also in designing the integral inequality technique [17,19] for time-varying delayed systems, which increase the order of uncorrelated augmentation [5,21,22]. Based on the discretized state, [10,27]'s piecewise analysis method is applied to confirm the system stability in whole delay bound. Asymmetric variation of the delay derivative is assumed so that direct extension to all constraints of the delay derivative can be achieved. Examples show the resulting criteria improve the allowable delay bounds over all existing ones in the literature.

Delay-Dependent H ∞ Filtering for Markovian Jump Time-Delay Systems: A Piecewise Analysis Method

A delay-dependent H∞ filtering for Markovian jump systems with time-varying delays is studied based on a piecewise analysis approach. Firstly, by exploiting delay partitioning-based Lyapunov function, a new delay-dependent criterion is derived for the H∞ performance analysis of the filtering-error systems, which can lead to much less conservative analysis results. Secondly, based on the criterion obtained, the gain of filter can be obtained in terms of linear matrix inequalities (LMIs). Finally, numerical examples are given to demonstrate the effectiveness of the proposed method.

Delay-Dependent Robust H∞ Output Tracking Control for Uncertain Networked Control Systems

AbstractIn this paper, the H∞ output tracking problem for networked control systems (NCSs) liable to model uncertainties and with delays varying within intervals is investigated. A new method is proposed to the robust H∞ output tracking analysis and control design for NCSs. The results presented here are an improvement over previous ones, for the analysis incorporates state-of-the-art stability techniques for systems with time-varying delays such as convex optimization technique, piecewise analysis method, and a new delay fractioning approach with the introduction of a novel auxiliary delayed state. The analysis is enriched with a numerical example that illustrates the advantages of our criteria which outperform previous criteria in the literature. Moreover, an illustrative example shows the effectiveness of the proposed H∞ output tracking control design.

Solution sensitivity for Karush–Kuhn–Tucker systems with non-unique Lagrange multipliers

This article is devoted to quantitative stability of a given primal-dual solution of the Karush–Kuhn–Tucker system subject to parametric perturbations. We are mainly concerned with those cases when the dual solution associated with the base primal solution is non-unique. Starting with a review of known results regarding the Lipschitz-stable case, supplied by simple direct justifications based on piecewise analysis, we then proceed with new results for the cases of Hölder (square root) stability. Our results include characterizations of asymptotic behaviour and upper estimates of perturbed solutions, as well as some sufficient conditions for (the specific kinds of) stability of a given solution subject to directional perturbations. We argue that Lipschitz stability of strictly complementary multipliers is highly unlikely to occur, and we employ the recently introduced notion of a critical multiplier for dealing with Hölder stability.

New criteria for synchronization stability of continuous complex dynamical networks with non-delayed and delayed coupling

The synchronization stability problem of general complex dynamical networks with non-delayed and delayed coupling is investigated based on a piecewise analysis method, the variation interval of the time delay is firstly divided into several subintervals, by checking the variation of derivative of a Lyapunov functional in every subinterval, several new delay-dependent synchronization stability conditions are derived in the form of linear matrix inequalities, which are easy to be verified by the LMI toolbox. Some numerical examples show that, when the number of the divided subintervals increases, the corresponding criteria can provide much less conservative results.

Robust [formula omitted] control for nonlinear systems over network: A piecewise analysis method

A piecewise analysis method (PAM) is proposed to investigate the H ∞ performance analysis and H ∞ control design for nonlinear networked control systems (NNCSs), which are presented in the form of T–S fuzzy model with time-varying input delay. Different from the existing method in dealing with the time-varying delay, the whole variation interval of the delay is divided into two subintervals with equal length. Respecting for the delay belonging each subinterval, new criteria on H ∞ performance analysis of the NNCSs are obtained by checking the variation of the derivative of the Lyapunov functional in the two subintervals. Then, criteria for the H ∞ controller design are obtained by using the convexity properties of the matrix inequality and some other new analysis techniques, which are shown in terms of nonlinear matrix inequalities and can be solved by using a cone complementarity liberalization method. As application of the derived results, H ∞ controller design is carried out for the nonlinear mass-spring system. Discussion shows that the proposed method is less conservative than the existing references.

An R function to non-parametric and piecewise analysis of competing risks survival data

Competing risks are frequently encountered in the analysis of survival data. Different methods of analysis can be used in estimated and comparing cumulative incidence functions provided enough information is available as to the times and causes of failure. Algorithms written in R have been developed to handle this type of data. In this paper we propose an R add-on function to the cmprsk package. This function is specifically oriented towards the non-parametric analysis of competing risk data and which provides analyses of three commonly used methods all in one program. We illustrate the use of this function with two examples in oncology and compare the estimates with those provided on the cmprsk and survival package.

Synchronization stability of continuous/discrete complex dynamical networks with interval time-varying delays

The synchronization problem of continuous/discrete general complex dynamical networks with time-varying delays is investigated. The delays considered in this paper are assumed to vary in an interval, where the lower and upper bounds are known. Based on a piecewise analysis method, the variation interval of the time delay is firstly divided into several subintervals, by checking the variation of derivative of a Lyapunov functional in every subinterval, then the convexity of matrix function method and the free-weighting matrix method are fully used in this paper. Some new delay-dependent synchronization stability criteria are derived in the form of linear matrix inequalities. Several numerical examples show that our method can lead to much less conservative results than those in the existing references.

Object orientation in two dimensional grasp with friction towards minimization of gripping power

This article reports an analysis of two dimensional grasp where a convex rigid object is grasped by two contact points with friction. The purpose is to find the object orientation that minimizes the norm of the contact force vector, each element of which is composed from the normal force and friction force at each contact point. The formulation of this problem requires some equality or inequality conditions. In the analysis, the solution of the equality conditions is parameterized at first. Based on the fact that the norm of the contact force vector becomes monotonic increasing function of this parameter, the minimal parameter values are calculated by means of the piecewise analysis. Using the relation between the friction coefficient and the apex angle of the friction cone effectively, the following result is obtained: the norm of the contact force, i.e, gripping power becomes locally minimal at the object orientation where the intersection point of the upper sides of two friction cones is located in opposite direction of the gravity from the center of mass of the grasped object.

Long-Term Mortality of Patients Undergoing Cardiac Catheterization for ST-Elevation and Non-ST-Elevation Myocardial Infarction

There are limited contemporary data comparing long-term outcomes after cardiac catheterization for ST-segment elevation myocardial infarction (STEMI) and non-STEMI (NSTEMI). We studied patients undergoing cardiac catheterization for STEMI (n=2413) and NSTEMI (n=1974) between 1999 and 2005 with at least 1 significant coronary lesion > or =75%. We compared adjusted mortality rates over restricted time intervals and the differential impact of early revascularization on mortality stratified by ST-elevation status. Between 1999 and 2007, 1274 patients died, with a median follow-up of 4 years. A piece-wise analysis showed a higher adjusted mortality risk for STEMI during the first 2 months (adjusted hazard ratio, 1.85; 95% confidence interval, 1.45 to 2.38) and a lower adjusted mortality risk for STEMI after 2 months (adjusted hazard ratio, 0.68; 95% confidence interval, 0.59 to 0.83). Compared with late or no revascularization, early revascularization was associated with a lower adjusted risk of mortality for both STEMI (adjusted hazard ratio, 0.73; 95% confidence interval, 0.58 to 0.90) and NSTEMI (adjusted hazard ratio, 0.76; 95% confidence interval, 0.65 to 0.89) (P for interaction=0.22). Among a contemporary cohort of acute MI patients with significant coronary disease during cardiac catheterization, STEMI was associated with a higher risk of short-term mortality, but NSTEMI was associated with a higher risk of long-term mortality. Early revascularization was associated with a similar improvement in long-term outcomes for both STEMI and NSTEMI. These data suggest that in clinical investigations of early revascularization among patients with NSTEMI, extended follow-up may be necessary to demonstrate treatment benefit.

Traceability and Verification of Interharmonic Generators in Support of Low-Frequency Immunity Testing (IEC61000-4-13)

A description of the interference immunity testing of electrical products is given, and the need for traceable calibration methods of the associated testing generators is described. A presentation of three analysis techniques to verify the respective testing modes of immunity testing generators is given, together with typical uncertainties. A deconvolution method developed for the phase characterization of the analog-to-digital converter (ADC) used in this work is reported. A least squares algorithm for the piecewise analysis of the International Electrotechnical Committee (IEC) flat-top waveform is presented in the Appendix.

Synchronization stability of general complex dynamical networks with time-varying delays: A piecewise analysis method

The synchronization problem of some general complex dynamical networks with time-varying delays is investigated. Both time-varying delays in the network couplings and time-varying delays in the dynamical nodes are considered. The delays considered in this paper are assumed to vary in an interval, where the lower and upper bounds are known. Based on a piecewise analysis method, the variation interval of the time delay is firstly divided into several subintervals, by checking the variation of the derivative of a Lyapunov function in every subinterval, then the convexity of matrix function method and the free weighting matrix method are fully used in this paper. Some new delay-dependent synchronization stability criteria are derived in the form of linear matrix inequalities. Two numerical examples show that our method can lead to much less conservative results than those in the existing references.

A Novel Distributed Simulation Approach in Adaptive Distance Relaying

In this paper, an adaptive distance relaying strategy based on the global network simulation (GNS) concept is presented. The GNS concept is actually a distributed simulation approach (DSA) for piecewise analysis of large-scale power grids using diakoptics and large change sensitivity (LCS) concepts. To set each utility's relays trip settings adaptively in each power system condition, detailed short circuit analysis is run in the GNS environment. It first updates the pre-fault voltage profile across utilities and then modifies their nodal ZBus in such a way to reflect the effect of the whole network in local fault studies performed by individual utilities; hence, presenting an accurate and secure federative approach on a geographically decomposed grid using local information and computational resources. A set of currently experienced rules in distance coordination is outlined and adaptive as well as conventional relay zone settings in each sub-network are calculated based on the selected rules. An efficient easy-to-implement algorithm to consider the effect of zero sequence mutual impedance among parallel lines is also presented and well integrated into the proposed adaptive approach in the GNS environment. The IEEE 14 bus test system and a real version of a large-scale grid with more than 2,600 buses are used to illustrate the characteristics of the proposed adaptive strategy in terms of security and dependability by comparison with conventional distance protection.

Delay-Dependent Stability Criteria for Systems with Time-Varying Delays: State Discretization Approach

A state-discretization approach [11], which was introduced for stability of constant delayed systems, will be extended to time-varying delayed systems. The states not only in constructing the Lyapunov-Krasovskii functional but also in designing the integral inequality technique [12] will be discretized. Based on the discretized-state, [9],[17]'s piecewise analysis method will be applied to confirm the system stability in whole delay bound. Numerical examples show that the results obtained by this criterion improve the allowable delay bounds over the existing results in the literature.

Mathematical Analysis on the Relation between Object Orientation and Contact Forces in the 2D Grasp with Frictions

This paper reports an analysis of 2D grasp where a convex rigid object is grasped by two contact points with frictions. The purpose is to find the object orientation that minimizes the norm of the contact force vector, each element of which is composed from the normal and friction force at each contact point. The formulation of this problem includes some equality or inequality conditions. In the analysis, the solution of the equality conditions is parameterized at first. Based on the fact that the norm of the contact force vector becomes monotonic increasing function of this parameter, the minimal parameter values are calculated by means of the piecewise analysis. Using the relation between the friction coefficient and the apex angle of the friction cone effectively, the following result is obtained: the norm of the contact force takes a local minimal value at the situation that the intersection point of the upper sides of each friction cones at two contact points is located in the opposite direction of the gravity from the center of mass of the grasped object.

A piecewise analysis method to stability analysis of linear continuous/discrete systems with time‐varying delay

AbstractThe delay‐dependent stability problem of linear continuous/discrete systems with time‐varying delay is investigated based on a piecewise analysis method (PAM). In the method, the variation interval of the time delay is firstly divided into several subintervals. By checking the variation of the Lyapunov functional in every subinterval, some new delay‐dependent stability criteria are derived. Several numerical examples show that our method can lead to much less conservative results than those in the existing references. Moreover, when the number of the divided subintervals increases, the corresponding criteria can provide an improvement on the results. Copyright © 2008 John Wiley & Sons, Ltd.

Piece-wise linear dynamic analysis of serpentine belt drives with a one-way clutch

A prototypical three-pulley serpentine belt drive with belt bending stiffness is extended to include a one-way clutch in order to understand the non-linear dynamics of the system with the one-way clutch performance. The clutch is modelled based on the relative velocity of the driven pulley and its accessory. The clutch locks (engages) the pulley and accessory for zero relative velocity and produces a positive inner clutch torque. Zero clutch torque initiates clutch disengagement, allowing unequal velocities of the two components. This model leads to a piece-wise linear system. The transition matrix is used to evaluate the system response in discrete time series for the two linear configurations, saving significant computational time. The system dynamics including response and dynamic tension drop are examined for varying excitation frequencies, inertia ratio of the pulley and accessory, and external load. The investigation of vibration reduction because of the single-direction power transmission of the clutch provides design guidelines in practice.

Switch-Type Hybrid Hard Decision Decoding Algorithms for Regular Low-Density Parity-Check Codes

This correspondence presents the switch strategies for switch-type hybrid hard decision decoding algorithms for regular low-density parity-check (LDPC) codes. After the piecewise analysis of extrinsic information transfer functions for Gallager decoding algorithm B (GB), the normalized switch scheme (NSS), for which the majority-based algorithms and GB are two examples, is proposed. Then, several other examples of NSSs are presented and their convergence properties are analyzed based on the extrinsic information transfer (EXIT) functions. In simulations, the proposed NSSs show meaningful performance improvements and less sensitivity to channel parameter underestimations compared with GB for small and moderate block length codes.

Piecewise analysis and modeling of circuit pack temperature cycling data

Temperature cycling environmental stress testing (EST) of circuit packs is a standard test procedure for the precipitation of latent defects in order to minimize early product lifecycle customer returns. EST is an expensive, energy-intensive bottleneck in the manufacturing process, one that is based on empiricisms that may be out of date. This presents great opportunity for optimization and test cost reduction. This paper describes the characterization of temperature cycling through analysis and modeling of process data in order to optimize the test parameters — ramp rate, temperature extremes, dwell times, and number of cycles. Failure data from circuit packs tested at a Lucent facility is analyzed using a regression technique and graphical inspection. The dwell and ramp periods of the test are considered in a piecewise manner. A cost model is applied based on distributions fitted to the failure data. The analysis yields a methodology for the dynamic, value-based optimization of temperature cycling EST.