Analysis Of Singular Systems Research Articles

Passivity analysis for singular systems with randomly occurring uncertainties via the event-based sliding mode control

This paper studies the passivity of the T–S fuzzy singular system with randomly occurring uncertainties via the event-based sliding mode control. The sliding surface function is designed such that the resulting sliding mode dynamics can be expressed by the considered system. Some sufficient conditions are proposed to guarantee the sliding mode dynamics is generalized admissible and robustly passive. Under the aperiodic sampled-data environment, the sliding mode control law is proposed via the event-triggered method. It guarantees that the state trajectory of the system can be driven onto the predefined sliding surface in a finite time and keep it forever. Finally, three examples are given to demonstrate the feasibility and superiority of the design method.

On Positive Realness for Stochastic Hybrid Singular Systems

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.

Control design for interval type-2 Takagi-Sugeno singular systems with time delay

In this work, the admissibility analysis and the control problem are investigated for nonlinear singular systems represented by interval type-2 Takagi-Sugeno (T-S) fuzzy models with time delay. First, the interval type-2 fuzzy singular systems with time delay have been described. Second, the admissibility analysis of the autonomous singular systems is studied. Third, the control problem has been investigated. For this, an interval type-2 fuzzy control law is designed to guarantee the admissibility of the closed-loop system despite the presence of uncertainties and time delay. To demonstrate the existence of the proposed controller, by using generalised integral inequalities, sufficient delay-dependent conditions are given in terms of Linear Matrix Inequalities (LMIs). Finally, an application to inverted pendulum system presented by interval type-2 fuzzy models is afforded to show the effectiveness of the suggested method.

New results on stability analysis for a kind of neutral singular systems with mixed delays

In this paper, the problem of the stability analysis for neutral singular systems with mixed delays is revisited. By the Lyapunov–Krasovskill functional approach and the singular system methodology, novel stability criteria are acquired, which can be easily expressed by linear matrix inequalities. First of all, in terms of Leibniz–Newton formula, zero equation with free-weighting matrices is fully constructed, which plays a key role in the field of stability analysis and makes the stability criterion feasible. Secondly, the asymptotically stability for neutral singular systems is strictly shown, which is different from other existing results. Thirdly, the regularity, non-impulsiveness and stability can be guaranteed based on some sufficient conditions. Finally, three numerical examples and simulation studies are presented to demonstrate the validity and feasibility of our method.

Damage quantification in moment resisting frame using phase space reconstructed from independent component sources

In the present study, a damage detection algorithm is proposed based on the amalgamation of independent component analysis (ICA) and phase space topology (PST) reconstruction. An experimental investigation is conducted by inducing damage in steel moment resisting frame (SMRF) and exciting it with ambient white noise base excitation. The experimental study is conducted for a healthy state and multiple progressive damage states. The damage in SMRF is manifested progressively by loosening the bolts of the beam-to-column and column-to-column bolted connections. The algorithm consists of two segments: In the first segment, the modal responses are obtained from the acquired response with the help of ICA. The optimal embedding parameters for modal responses are evaluated with the help of average mutual information function and singular system analysis. The second segment deals with the reconstruction of PST with the help of modal responses and embedding parameters. Lastly, the damage sensitive features (DSFs) are evaluated to identify and quantify the induced damage. The DSFs evaluated in the present study are, namely, (a) change in phase space topology (CPST), (b) Mahalanobis distance between phase space topology (MDPST), and (c) Itakura distance (ID). The CPST and MDPST measure the dissimilarity between the PSTs of healthy and damage states, whereas ID measures the dissimilarity between the set of auto-regressive coefficients of healthy and damage states of SMRF. The DSFs are able to detect and quantify the commencement and evolution of the damage in the SMRF subjected to ambient base excitation.

Stability analysis of stochastic switching singular systems with jumps

This paper deals with the stability problem of a class of stochastic switching singular systems with jumps, where all the continuous subsystems can be unstable. By introducing multiple time-varying discretized Lyapunov functions and designing novel switching signals via mode-dependent dwell times, sufficient conditions ensuring mean square and almost sure stabilities of the considered systems are obtained. On the basis of these findings, some existing results in the literature are further generalized. We finally provide a numerical example to verify the applicability of the proposed theoretical results.

Investigating the semiannual oscillation on Mars using data assimilation

A Martian semiannual oscillation (SAO), similar to that in the Earth’s tropical stratosphere, is evident in the Mars Analysis Correction Data Assimilation reanalysis dataset (MACDA) version 1.0, not only in the tropics, but also extending to higher latitudes. Unlike on Earth, the Martian SAO is found not always to reverse its zonal wind direction, but only manifests itself as a deceleration of the dominant wind at certain pressure levels and latitudes. Singular System Analysis (SSA) is further applied on the zonal-mean zonal wind in different latitude bands to reveal the characteristics of SAO phenomena at different latitudes. The second pair of principal components (PCs) is usually dominated by a SAO signal, though the SAO signal can be strong enough to manifest itself also in the first pair of PCs. An analysis of terms in the Transformed Eulerian Mean equation (TEM) is applied in the tropics to further elucidate the forcing processes driving the tendency of the zonal-mean zonal wind. The zonal-mean meridional advection is found to correlate strongly with the observed oscillations of zonal-mean zonal wind, and supplies the majority of the westward (retrograde) forcing in the SAO cycle. The forcing due to various non-zonal waves supplies forcing to the zonal-mean zonal wind that is nearly the opposite of the forcing due to meridional advection above ∼3 Pa altitude, but it also partly supports the SAO between 40 Pa and 3 Pa. Some distinctive features occurring during the period of the Mars year (MY) 25 global-scale dust storm (GDS) are also notable in our diagnostic results with substantially stronger values of eastward and westward momentum in the second half of MY 25 and stronger forcing due to vertical advection, transient waves and thermal tides.Mars; Mars, atmosphere; Mars, climate; Atmospheres, dynamics; Atmospheres, structure; Meteorology.

Convex Stability Analysis of Nonlinear Singular Systems via Linear Matrix Inequalities

Stability analysis of nonlinear singular systems, arising from differential algebraic equations, is addressed in this paper, exploiting the fact that it belongs to the class of Positvstellensatz problems. By means of the direct Lyapunov method and a variety of convex descriptor forms, sufficient conditions in terms of linear matrix inequalities are developed. Issues concerning proper initialization and simulation are also considered. Illustrative examples are provided.

Coulomb Gas Analogy: A Statistical Physics Approach to Performance Analysis of MIMO Systems

In this correspondence, by adopting the Coulomb gas analogy that is an analytical approach from statistical physics, we derive a closedform approximation of the cumulative distribution function (CDF) of the largest eigenvalue of a random Gram matrix H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</sup> H, where H denotes the channel matrix of a multiple-input multiple-output (MIMO) system. The expression of approximation has a simple structure in terms of several elementary functions, which is derived by assuming that the entries of H have Nakagami-m distributed amplitude with an independent phase. This assumption is made because it applies in two common cases of the Nakagami-m distributions, i.e., with a uniformly distributed phase and a complex signal model. Simulation results indicate that the theoretical expression also provides a good approximation to the CDF for Rice and Hoyt distributions when the CDF is within a near-one range. This range takes the form of (P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">no</sub> ,1), where we assume P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">no</sub> = 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> by default in this study. The derived approximation can find many uses for the performance analysis of MIMO beamforming and singular value decomposition MIMO systems, e.g., evaluating the outage probability for these systems.

Event-based mixed ℋ ∞ and passive filtering for discrete singular stochastic systems

ABSTRACT This work devotes to the event-based mixed and passive filter analysis and design problems of discrete-time singular stochastic network systems with Markovian jump parameters. Using the event-triggered communication approach, we first derive a network-induced delay discrete error singular stochastic network model. With the help of event-triggered method and stochastic Lyapunov function scheme, sufficient conditions are then established such that the resulting error stochastic model is regular, causal, stochastically mean-square stable with a mixed and passivity performance index. By applying slack matrix variables and filter transfer function equivalent method, an event-triggered mixed and passive filter is designed such that the resulting error singular stochastic network system satisfies certain mixed and passive filter performance index, and the derived conditions could be solved in terms of linear matrix inequality method. Finally, the effectiveness of the proposed methods is illustrated by a numerical example.

New results on dissipativity analysis of singular systems with time-varying delay

This paper focuses on the dissipativity analysis of singular systems with time-varying delay. The objective is to obtain a less conservative criterion with less computational demand. Based on the state decomposition method, singular systems are rewritten as differential subsystems and algebraic ones. First of all, the components of state vectors are applied to design a novel Lyapunov–Krasovskii functional (LKF) for the differential subsystems. Then, in the derivative of the LKF, the algebraic ones are introduced and the Wirtinger-based integral inequality together with the extended reciprocally convex matrix inequality is adopted to estimate the single integral term. Therefore, a new dissipativity criterion is obtained, which realizes both less conservativeness and less computational demand. Finally, two numerical examples are given to verify the superiority of the proposed method.

A delay-range-dependent stabilization of uncertain singular time-delay systems with one-sided Lipschitz nonlinearities subject to input saturation

This paper investigates the problem of delay-range-dependent robust stabilization for nonlinear singular systems with time-delay subject to some constraints. In practice, the control problem of dynamic systems faces a variety of constraints such as: presence of input saturation; one-sided Lipschitz nonlinearities; model uncertainties; and time-varying delay. The interaction of both algebraic and differential equations in singular systems with delayed state variables adds some complexities and difficulties in the procedure of analysis and design of singular time-delay systems. Moreover, the one-sided Lipschitz nonlinearity condition, which is less conservative than the well-known Lipschitz condition, is considered while the presence of actuator saturation also imposes additional complexity in the procedure of controller design. In this regard, by choosing an appropriate Lyapunov–Krasovskii functional with applying the free-weighting matrices approach, the sufficient conditions are derived as linear matrix inequalities which guarantee the asymptotic stability of the resulting uncertain closed-loop singular system. Finally, computer simulations are provided to verify the theoretical results.

Damage Detection Using Dissimilarity in Phase Space Topology of Dynamic Response of Structure Subjected to Shock Wave Loading

Shockwave is a high pressure and short duration pulse that induce damage and lead to progressive collapse of the structure. The shock load excites high-frequency vibrational modes and causes failure due to large deformation in the structure. Shockwave experiments were conducted by imparting repetitive localized shock loads to create progressive damage states in the structure. Two-phase novel damage detection algorithm is proposed, that quantify and segregate perturbative damage from microscale damage. The first phase performs dimension reduction and damage state segregation using principal component analysis (PCA). In the second phase, the embedding dimension was reduced through empirical mode decomposition (EMD). The embedding parameters were derived using singular system analysis (SSA) and average mutual information function (AMIF). Based, on Takens theorem and embedding parameters, the response was represented in a multidimensional phase space trajectory (PST). The dissimilarity in the multidimensional PST was used to derive the damage sensitive features (DSFs). The DSFs namely: (i) change in phase space topology (CPST) and (ii) Mahalanobis distance between phase space topology (MDPST) are evaluated to quantify progressive damage states. The DSFs are able to quantify the occurrence, magnitude, and localization of progressive damage state in the structure. The proposed algorithm is robust and efficient to detect and quantify the evolution of damage state for extreme loading scenarios.

Stability analysis for positive singular systems with distributed delays

This paper is concerned with the stability analysis for continuous-time positive singular systems with distributed delays. By introducing an auxiliary system, a necessary and sufficient positivity condition is proposed for singular systems with distributed lags. Based on this condition, we present a sufficient stability condition for positive singular systems with distributed delays and extend the result to systems with distributed delays over a bounded time-varying interval. In addition, this stability condition is also necessary when strictly positive initial conditions are available. Numerical simulations are utilized to illustrate the effectiveness of our results.

Stability Analysis for Positive Singular Systems With Time-Varying Delays

This paper is concerned with the stability analysis for continuous-time positive singular systems with time-varying delays. First, an auxiliary system is introduced to establish the positivity condition for singular time-delay systems. Based on the positivity condition, the stability criterion is obtained for the positive singular systems with constant delays. By analyzing the monotonic property of the system trajectory, we extend the stability condition to the cases with time-varying delays. A numerical simulation is employed to illustrate the effectiveness of our results.

Dissipative analysis for nonlinear singular systems with time-delay

This paper is concerned with the dissipative control problem for a class of nonlinear singular systems with time-delay. The quadratic supply rate with coefficient matrix Q > 0 and Q ≤ 0 are both discussed. Based on the Lyapunov stability theory, sufficient conditions are given to guarantee that the system is strictly dissipative via linear matrix inequality technique. Then congruent transformation method and Schur complement lemma are respectively used to determine corresponding proportional and derivative feedback controller for Q > 0 and Q ≤ 0. At last, two examples involve a practical example are given to verify the effectiveness of the method proposed in this paper.

L∞-gain analysis for positive singular time-delay systems

This paper is devoted to the characterization of L∞-gain for positive singular systems with time-varying delays. First, we introduce an augmented system to replace the original system in order to analyze the positivity of singular systems with time-varying delays. By investigating the monotonicity of state trajectory, the L∞-gain for singular system with constant delays is characterized. Then, by comparing the trajectories of time-varying delay system and constant delay case, we finally propose the L∞-gain for singular system with time-varying delays. It is shown that the L∞-gain of positive singular systems is independent of the magnitude of delays.

Dissipative analysis for network-based singular systems with non-fragile controller and event-triggered sampling scheme

This paper investigates the problem of dissipative based non-fragile controller for network-based singular systems with event-triggered sampling scheme. Based on the Lyapunov–Krasovskii functional approach which fully uses the available information about the actual sampling pattern, a new set of sufficient conditions is obtained to guarantee that the closed-loop network-based singular systems are regular, impulsive free, asymptotically stable and strictly (Q,S,R)−θ dissipative. Moreover, a design algorithm for the desired controller with event-triggered sampling scheme is formulated in terms of linear matrix inequalities. By solving an optimization problem with some inequality constraints, the explicit expression of the non-fragile controller gain matrix is characterized to achieve the required result. Finally, two numerical examples are provided to demonstrate the effectiveness and superiority of the proposed control design scheme.

Fuzzy-model-based admissibility analysis and output feedback control for nonlinear discrete-time systems with time-varying delay

This paper is concerned with the admissibility analysis and stabilization problems for singular fuzzy discrete-time systems with time-varying delay. The novelty of this paper comes from the consideration of a new summation inequality which is less conservative than the usual Jensen inequality, the Abel-Lemma based inequality and the Seuret inequality. Based on the inequality, sufficient conditions are established to ensure the systems to be admissible. Moreover, the corresponding conditions for the existence of desired static output feedback controller gains are derived to guarantee that the closed-loop system is admissible. The conditions can be solved by a modified cone complementarity linearization (CCL) algorithm. Examples are given to show the effectiveness of the proposed method.

Stability analysis of uncertain singular systems

Uncertain singular system, described as a multi-dimensional uncertain differential equation, is a kind of singular system disturbed by canonical process. Stability analysis has been widely investigated while nobody has ever considered the stability of uncertain singular systems. In this paper, three different styles of stabilities called stability in mean, stability in measure and almost sure stability of uncertain singular systems are studied. These stabilities can be employed to illustrate the internal character of uncertain singular systems in different aspects. Several sufficient conditions are presented to judge the above stabilities. An example is given to show the effectiveness of the results obtained.