Nonlinear Singular Systems Research Articles

Leader‐following consensus of nonlinear singular multiagent systems with intermittent communication

This paper investigates the leader‐following consensus of nonlinear singular multiagent systems with intermittent communication on a fixed undirected topology. Unlike the existing works on singular multiagent systems that the communication among agents is continuous, in this work, agents can only communicate with their neighbors on some disconnected time intervals. Based on algebraic graph theory, singular system theory and multi‐Lyapunov function approach, the cooperative intermittent control protocol and sufficient conditions are proposed to guarantee the existence and uniqueness of solutions and leader‐following consensus of the systems. Furthermore, a description of state jumps at the instants of communication interrupt and restoration is presented. Finally, numerical examples are provided to illustrate the effectiveness of the theoretical analysis.

Robust observer-based sliding mode control for nonlinear uncertain singular systems with time-varying delay and input non-linearity

This article focuses on the output-feedback sliding mode control design problem for a class of non-linear singular systems with time-varying delay and uncertainties. More precisely, we aim to design an adaptive observer-based sliding mode controller for such class of systems. The appealing aspects of this approach include (i) based on an appropriate Lyapunov–Krasovskii functional, a delay-dependent sufficient condition is established to guarantee the autonomous singular system to be admissible and (ii) by constructing an observer to estimate the system states, an integral sliding mode surface and an adaptive observer-based sliding mode controller are designed to ensure the closed-loop singular system to be insensitive to all admissible uncertainties and satisfies the reaching condition. The developed results are tested on three representative examples to illustrate the theoretical developments.

Observer-Based H-infinity Controller for Nonlinear Singular Networked Control Systems

Observer-Based H-infinity Controller for Nonlinear Singular Networked Control Systems

Robust Impulsive Stabilization of Uncertain Nonlinear Singular Systems with Application to Transportation Systems

We consider the robust asymptotical stabilization problem for uncertain singular systems. We design a new impulsive control technique to ensure that the controlled singular system is robustly asymptotically stable and hence derive the corresponding stability criteria. These sufficient conditions are expressed in the form of algebra matrix inequalities and can be implemented numerically. We finally provide a numerical example of a transportation system to illustrate the effectiveness and usefulness of the proposed criteria.

Analysis of iterative learning control for one-sided Lipschitz nonlinear singular systems

This paper deals with the problem of iterative learning control for a class of singular systems with one-sided Lipschitz nonlinearity. In order to track the given desired trajectory, a closed-loop D-type learning algorithm is proposed for such nonlinear singular systems. Then the convergence result is derived by utilizing the one-sided Lipschitz and quadratically inner-bounded conditions. In this work, the main contribution is to apply the iterative learning approach to one-sided Lipschitz singular systems, while most researches are focus on the Lipschitz systems. It is shown that the algorithm can guarantee the system output converges to the desired trajectory on the whole time interval. Finally, the effectiveness of the presented algorithm is verified by a numerical example.

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.

Reachable set estimation and dissipativity for discrete-time T–S fuzzy singular systems with time-varying delays

This paper studies the problems of reachable set estimation and dissipativity analysis for a class of nonlinear singular system with time-varying delays and bounded input disturbances. The nonlinear singular system is modeled by Takagi–Sugeno (T–S) fuzzy singular delay system. Firstly, based on new Lyapunov–Krasovskii functional, in which the difference of triple-summable terms and both the upper and the lower bound of time-varying delays are considered, and by using the free-weighting matrix technique, reciprocally convex combination approach, a new delay-dependent reachable set estimation and dissipativity condition is obtained. Furthermore, the derived condition can be converted into linear matrix inequalities (LMIs), and it can guarantee the reachable set to be bounded by the intersection of ellipsoids and the T–S fuzzy singular delay system is strictly (G1,G2,G3)−δ̃−dissipative. Finally, a numerical example is provided to demonstrate the effectiveness of the obtained results in this paper.

Singular linear systems on Lie groups; equivalence

In this paper, we define different kinds of singular systems on Lie groups and we analyze some of them. Furthermore, we state sufficient conditions for a general nonlinear singular system defined on a manifold to be equivalent by diffeomorphism to one of these models. Some examples are computed.

A Robust H∞ Filter for Uncertain Continuous-Time Affine Nonlinear Singular Systems

In the present paper, the problem of robust H∞ filtering for continuous-time affine nonlinear singular systems (ANSSs) with norm-bounded uncertainty is studied. Employing Luenberger-like and certainty equivalent structures, and based on the differential game theory, sufficient conditions for the existence of such filters are derived. These conditions are in the form of a generalized Hamilton–Jacobi–Isaacs (GHJI) inequality and the output injection gain of each filter is obtained as a function of the corresponding GHJI inequality solution. Numerical simulations are provided to demonstrate the applicability of the proposed approach. The results show that the adopted method not only perfectly achieves the estimation goals in the presence of model uncertainties but also outperforms some existing results for known (certain) systems.

Admissibility Analysis for Interval Type-2 Fuzzy Descriptor Systems Based on Sliding Mode Control.

This paper is concerned with the sliding mode control of nonlinear singular systems in terms of the interval type-2 (IT2) fuzzy model. To better approximate the nonlinear systems, the modeling errors are considered in the IT2 fuzzy model. The uncertainties in membership functions are expressed based on their boundedness. Admissibility conditions are obtained via a linear matrix inequalities approach. A new reaching law-based sliding controller is presented by choosing a typical sliding surface to analyze the sliding motion, such that all of the input gains are allowed to be different and the chattering of the system can be minimized with a guaranteed H∞ performance. The feasibility of the proposed control method is verified by simulation results.

Finite-time H∞ control for a class of discrete-time nonlinear singular systems

This paper investigates the finite-time control problems for a class of discrete-time nonlinear singular systems via state undecomposed method. Firstly, the finite-time stabilization problem is discussed for the system under state feedback, and a finite-time stabilization controller is obtained. Then, based on which, the finite-time H∞ boundedness problem is studied for the system with exogenous disturbances. Finally, an example of population distribution model is presented to illustrate the validity of the proposed controller. Because there is no any constraint for singular matrix E in the paper, controllers can be designed for more discrete-time nonlinear singular systems.

Iterative learning control for a class of singular impulsive systems

ABSTRACTIn this paper, the iterative learning control problem for a class of nonlinear singular impulsive systems is discussed. Then, a D-type (derivative-type) iterative learning control algorithm is presented such that the output tracks the desired output trajectory as accurate as possible. Furthermore, the sufficient condition for the convergence of the proposed algorithm is established in detail. Finally, a numerical example is included to corroborate the theoretical analyses.

Resilient control based on disturbance observer for nonlinear singular stochastic hybrid system with partly unknown Markovian jump parameters

In this paper, the composite anti-disturbance resilient control is considered for nonlinear singular stochastic hybrid system with partly unknown Markovian jump parameters under multiple disturbances. Three kinds of disturbances are included in the studied system. One is generated by an external system and it enters the hybrid system from the channel of the control input. The other one is stochastic white noise. And the third one is the external unknown time-varying disturbance and it is supposed to be H2 norm bounded. By combining the disturbance-observer-based-control scheme, H∞ control technique and resilient control method, a composite anti-disturbance resilient controller is constructed to attenuate and eliminate the affection of these disturbances, and ensures the whole closed-loop system regular, impulse free and stochastically stable with the corresponding control performance. Then, some sufficient conditions and the gains of the controller and observer are obtained by using Lyapunov function method and the linear matrix inequalities (LMIs) technique. Finally, two numerical examples are given to show the effectiveness of presented method.

Neuro-heuristics for nonlinear singular Thomas-Fermi systems

A neuro-heuristic scheme is design to solve nonlinear singular second order system based on Thomas-Fermi equation using the strength of universal approximation capabilities of feedforward artificial neural networks supported with optimization power of genetic algorithms and sequential quadratic programming. An error function is constructed by differential equations artificial neural networks and optimization of design parameters of networks is carried out initially with genetic algorithms for the global search while sequential quadratic programming algorithm is used for further rapid local refinements. The performance of the design is analyzed by solving variants of Thomas-Fermi equation. Comparison of the results with standard numerical as well as analytical solvers establish the significance of the method on the basis of accuracy and convergence through statistical performance indices.

Mixed filter design for nonlinear singular Markovian jump systems with time-varying delays based on a dissipativity performance index

This paper deals with the problem of dissipative filtering for a class of nonlinear singular Markovian Jump systems (SMJSs) with time-varying delays. Our consideration is centered on the design of a mixed filter that can contain both mode-dependent and mode-independent filters in a unified framework. By using a delay-decomposition approach and constructing a mode-dependent stochastic Lyapunov–Krasovskii functional, sufficient delay-dependent conditions are derived in terms of linear matrix inequalities, which guarantee the considered nonlinear SMJSs to be stochastically admissible with a dissipativity performance [Formula: see text]. Based on the conditions, the existence conditions and parameters of the desired filter are obtained. Two numerical examples are given to illustrate the reduced conservatism and the effectiveness of the proposed methods.

Sampled-data control for nonlinear singular systems based on a Takagi–Sugeno fuzzy model

The sampled-data admissibility problem for nonlinear singular systems in Takagi–Sugeno fuzzy models is discussed. By adding some novel terms, a novel fuzzy time-dependent Lyapunov–Krasovskii functional is proposed to fully capture the available characteristics of the actual sampling pattern. Sufficient conditions are derived to determine the regularity, absence of impulses and asymptotic stability of the system by using Lyapunov stability theorems. Then, the fuzzy sampled-data controller is obtained by analysing the admissible condition. One practical example involving a truck–trailer system is considered. It is shown that the proposed method and the designed controller for the system are effective and that less conservativeness can be obtained.

Robust finite-time stability of singular nonlinear systems with interval time-varying delay

The problem of robust finite-time stability (RFTS) for singular nonlinear systems with interval time-varying delay is studied in this paper. Some delay-dependent sufficient conditions of RFTS are derived in the form of the linear matrix inequalities (LMIs) by using Lyapunov–Krasovskii functional (LKF) method and singular analysis technique. Two examples are provided to show the applications of the proposed criteria.

SOLVABILITY FOR NONLINEAR SINGULAR FRACTIONAL DIFFERENTIAL SYSTEMS WITH MULTI-ORDERS

In this paper, we consider the existence of positive solutions for a class of nonlinear singular fractional differential systems with multi-orders. Our analysis relies on fixed point theorems on cones. Some sufficient conditions for the existence of at least one or two positive solutions for boundary value problem of nonlinear singular fractional differential systems with multi-orders are established. As an application, an example is presented to illustrate the main results.

Existence results for Kirchhoff type systems with singular nonlinearity

Using the method of sub-super solutions, we study the existence of positive solutions for a class of singular nonlinear semipositone systems involving nonlocal operator.

Semi‐Global Robust Output Regulation for A Class of Singular Nonlinear Systems with Unknown Algebraic Equations

AbstractThis paper considers semi‐global robust output regulation problem for a class of singular nonlinear systems whose algebraic equations are not precisely known. Since the algebraic equations are not known, the output regulation problem of singular nonlinear systems cannot be solved by directly reducing the singular nonlinear system into a normal nonlinear system. Based on internal model principle, we convert the robust output regulation problem of singular nonlinear systems into a robust stabilization problem of an augmented singular nonlinear system. The augmented singular nonlinear system is also with unknown algebraic equations. However, without transforming the singular nonlinear system into a normal nonlinear system, it is shown that the augmented singular nonlinear system can be semi‐globally stabilized by a high gain output feedback control law under some reasonable assumptions. Moreover, the semi‐global stabilization control law of the augmented singular nonlinear systems also solves the semi‐global robust output regulation problem of the original singular nonlinear system.