Class Of Nonlinear Singular Systems Research Articles

Further results on the finite-time static output feedback control for nonlinear singular systems

This paper studies the finite-time static output feedback control for a class of nonlinear singular systems. Finite-time stability criterion for the closed singular systems is proposed by static output feedback technique. Based on the properties of structure of the singular system, static output feedback control gain is obtained by using singular value decomposition technique. Meanwhile, different from the existing results of normal systems, the presented scheme reduces the conservatism and complexity during the calculation process. Furthermore, static output feedback H∞ controller is designed and finite time stability criterion is proposed for the nonlinear singular systems with external disturbance. Finally, the applicability and effectiveness of the proposed strategy are illustrated by a circuit system simulation.

Sampled-Data Control for a Class of Singular Takagi-Sugeno Fuzzy Systems with Application in Truck-Trailer System

In order to solve the admissibility problem for a class of nonlinear singular systems with sampling, nonlinearity, and external disturbances, a sample-data control algorithm based on input delay methodology is proposed in this paper. Firstly, the system is converted to a time-delay system based on Takagi–Sugeno fuzzy models via an input delay approach, with many novel time-delay methods being used to deal with the sampled-data control problem. Secondly, both the upper and lower bounds of the sampling period are considered, which has a wider application scope. Thirdly, to obtain less conservative results, an appropriate Lyapunov–Krasovskii function, which involves several symmetric positive definite matrices, is established, and a relaxation variable is introduced by the method of reciprocally convex inequality. Then the conditions of admissibility are given, and the design method of the sampled-data controller is introduced. Finally, a truck-trailer example and two numerical examples are given to prove that the proposed approaches are valid and applicable.

On qualitative behaviors of nonlinear singular systems with multiple constant delays

This paper deals with some qualitative properties of a class of nonlinear singular systems with multiple constant delays. Via the Lyapunov-Krasovskii functional (LKF) method and integral inequalities, we obtain some new sufficient conditions which guarantee that the considered systems are regular, impulse-free and exponentially stable. Two numerical examples are given to illustrate the applicability of the obtained results using MATLAB software. By this work, we extend and improve some results of the past literature.

The Approximation of the Nonlinear Singular System with Impulses and Sliding Mode Control via a Singular Polynomial Fuzzy Model Approach

In this paper, the Singular-Polynomial-Fuzzy-Model (SPFM) approach problem and impulse elimination are investigated based on sliding mode control for a class of nonlinear singular system (NSS) with impulses. Considering two numerical examples, the SPFM of the nonlinear singular system is calculated based on the compound function type and simple function type. According to the solvability and the steps of two numerical examples, the method of solving the SPFM form of the nonlinear singular system with (and without) impulse are extended to the more general case. By using the Heine–Borel finite covering theorem, it is proven that a class of nonlinear singular systems with bounded impulse-free item (BIFI) properties and separable impulse item (SII) properties can be approximated by SPFM with arbitrary accuracy. The linear switching function and sliding mode control law are designed to be applied to the impulse elimination of SPFM. Compared with some published works, a human posture inverted pendulum model example and Example 3.2 demonstrate that the approximation error is small enough and that both algorithms are effective. Example 3.3 is to illustrate that sliding mode control can effectively eliminate impulses of SPFM.

Sliding Mode Control for a Class of Nonlinear Singular Systems With Partly Immeasurable Premise Variables

This paper investigates the problem of sliding mode controller design for a class of T-S fuzzy singular systems (TSFSSs) with partly immeasurable premise variables. By analyzing the different cases of immeasurable premise variables, novel state-feedback, and static output-feedback-based sliding mode controllers design methods are first developed. The information of measurable premise variables in TSFSS is utilized to design the controllers. Attention is focused on solving the problem of sliding mode controllers design for TSFSS with immeasurable premise variables related to time and system states. Further, based on the new sliding mode control (SMC) methods, some new convex conditions for designing sliding mode controllers are proposed. It is shown that the proposed sliding mode controllers design approaches have the advantage over existing SMC methods to stabilize the TSFSS with immeasurable premise variables. Finally, two simulation results are given to verify the feasibility and effectiveness of the proposed methods.

Finite-time stochastic input-to-state stability and observer-based controller design for singular nonlinear systems

This paper investigated observer-based controller for a class of singular nonlinear systems with state and exogenous disturbance-dependent noise. A new sufficient condition for finite-time stochastic input-to-state stability (FTSISS) of stochastic nonlinear systems is developed. Based on the sufficient condition, a sufficient condition on impulse-free and FTSISS for corresponding closed-loop error systems is provided. A linear matrix inequality condition, which can calculate the gains of the observer and state-feedback controller, is developed. Finally, two simulation examples are employed to demonstrate the effectiveness of the proposed approaches.

Observer‐based adaptive neural control for a class of nonlinear singular systems

SummaryThe problem of observer‐based adaptive neural control via output feedback for a class of uncertain nonlinear singular systems is studied in this article. The nonlinear singular systems can be regarded as two subsystems that are coupled with each other: differential subsystem and algebraic subsystem. The differential systems can be nonstrict feedback structures. To guarantee that the singular system is regular and impulse‐free, two new conditions are proposed. By the conditions, the linear controller and observer, which are used to estimate the immeasurable state variables, are obtained. Then, an output feedback scheme through adaptive neural backstepping is proposed to ensure that all states of the closed‐loop system are semiglobally uniformly ultimately bounded and converge to a small neighborhood of the origin. Simulation examples illustrate the effectiveness of the presented method.

Finite-Time Stabilization for a Class of Nonlinear Singular Systems

The finite-time stabilization problem for a class of nonlinear singular systems is studied. Under the assumption that the considered system is impulse controllable, a sufficient condition is provided for the design of a state feedback control law guaranteeing the finite-time stability of the closed-loop system, and an explicit expression of the state feedback gain is also given. The proposed criterion is expressed in terms of strict matrix inequalities which is easy to be verified numerically. A numerical example is given to illustrate the effectiveness of the proposed method.

Proportional-Difference Observer Design for Singular Systems in an LMI Framework

This paper deals with the problem of proportional-difference observer design for singular systems in the discrete-time domain. Several necessary and sufficient conditions for the existence and convergence of the proposed observer are given and proved. Without using any additional transformations, a necessary and sufficient condition for the solvability of this problem is obtained in terms of linear matrix inequalities. The explicit expression of desired observer is also given. Furthermore, an extension to a class of nonlinear singular systems with Lipschitz constraints is investigated. Finally, a practical example and a numerical one are simulated to illustrate the effectiveness of the proposed approaches.

Homotopy Perturbation Method for a Class of Nonlinear Singular System of Initial Value Problems

In this paper, a method based on homotopy perturbation method is used to establish the recursive scheme for the solution of nonlinear singular system of initial value problems. The convergence analysis of the proposed method is also shown. The accuracy and efficiency of the proposed method are demonstrated through various examples.

The approximation of the T–S fuzzy model for a class of nonlinear singular systems with impulses

The present paper solves the approximation problem of T–S fuzzy linear singular system for a class of nonlinear singular system with impulses. Consider a special nonlinear singular bio-economic system with impulses; the T–S fuzzy linear singular system of the nonlinear singular system has been calculated. The relationship between the impulse of the singular system and the singular induced bifurcation is proved for the first time. For this particular case, it is extended to more generally nonlinear singular system. For a class of nonlinear singular system that is bounded impulse-free item and separable impulse item with singularity-induced bifurcation, we proved that it can be approximated by T–S fuzzy singular system with arbitrary accuracy. Finally, a numerical simulation is carried out to show the consistency with theoretical analysis and illustrate the effectiveness of approximation.

Adaptive Robust H∞ Sliding Mode Control for Singular Systems with Time-varying Delay and Uncertain Derivative Matrix

This paper considers the problem of sliding mode control (SMC) design for a class of nonlinear singular systems with time-varying delay and uncertainties, especially with uncertainties in the derivative matrix. By taking uncertainties of the derivative matrix into account, the state augmentation transformation is constructed such that uncertainties of the derivative matrix are eliminated. Then an appropriate integral-type sliding surface function is designed. And the resulting sliding mode dynamics is an uncertain singular time-varying delay system. A delay-dependent sufficient condition which guarantees the sliding mode dynamics to be admissible with H∞ performance is established. A new version of stabilization solvability condition is then proposed in terms of linear matrix inequality (LMI), which determines the undetermined parameter K in both the sliding surface function and the SMC laws. Moreover, two distinctive controllers (i.e., a SMC law and an adaptive SMC law) are synthesized such that the finite-time reachability of the predesigned sliding surface can be ensured. Finally, simulation examples are given to demonstrate the effectiveness and the merits of the proposed theory.

The approximation of the T–S fuzzy model for a class of nonlinear singular system with derivative of input

In this paper, the approximation problem of T–S fuzzy linear singular system for a class of nonlinear singular system with derivative of input is considered and the nonlinear singular system has impulses. Consider a numerical example and a two-wheel drive robot, the T–S fuzzy singular systems are calculated for original system with derivative of input. According to solvability and steps of solving of the two examples, the results are extended to more generally nonlinear singular system with derivative of input. The theorem and algorithm that are given if input-state system is bounded impulse-free item and separable impulse item, it can be approximated by T–S fuzzy singular system with arbitrary accuracy. Finally, a numerical simulation is carried out to show the consistency with theoretical analysis and illustrate the effectiveness of approximation.

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.

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.

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.

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.

A nonlinear Luenberger-like observer for nonlinear singular systems

This paper investigates observer design problem for a large class of nonlinear singular systems with multiple outputs. We first regularize the singular system by injecting the derivative of outputs into the system. Then differential geometric method is applied to transform the regularized system into a simple normal form, for which a Luenberger-like observer is proposed.

Semi-global robust output regulation for a class of singular nonlinear systems via nonlinear internal model

ABSTRACTMost of existing results on robust output regulation problem of singular nonlinear systems are limited to local solutions. In this paper, the semi-global robust output regulation problem for a class of singular nonlinear systems is investigated by using a nonlinear internal model. Attaching a nonlinear internal model to the singular nonlinear system yields an augmented singular nonlinear system whose semi-global robust stabilisation solution leads to the solution of the semi-global robust output regulation problem of the original singular nonlinear system. The solvability conditions of the semi-global output regulation problem are established by addressing the solvability of the robust stabilisation problem of augmented singular nonlinear system. Finally, a numerical simulation example is used to illustrate the design of the semi-global regulator for the singular nonlinear systems.

H∞filtering for a class of singular biological systems

This study deals with the H ∞ filtering problem for a class of singular biological systems with stochastic exogenous disturbance. Singular system theory is utilised to build a stochastic singular food chain system. The authors’ purpose is to estimate the unmeasurable state variables of the food chain system by the available measurements. The general condition is established for a class of non-linear singular systems to achieve input-to-state stable in mean and the prescribed H ∞ performance level. A sufficient condition of the solvability of filtering problem is proposed for the singular food chain system. Simulation example is provided to illustrate the effectiveness of the proposed filtering approach developed in this study.