Stability Of Singular Systems Research Articles

Dynamic feedback H ∞ optimal control for singular systems

Time delay and packet loss often occur in the process of information transmission in descriptor systems, and H∞ optimal control is adopted to deal with this phenomenon. Firstly, the stability of singular systems is proved by using Lyapunov function, secondly, the existence of H∞ controller and-suboptimal control are proved, and finally, the necessary and sufficient condition of H ∞-optimal controller is proved. The validity and feasibility of the proposed method are verified by numerical simulation.

Event‐triggered H‐infinity stabilization for singular systems with state delay

AbstractThis paper is concerned with the problems of stability analysis, controller design, and H∞ control for singular systems with state delay and disturbance based on event‐triggered control. Firstly, the corresponding model of this system is proposed, taking into consideration issues of regular, impulse free, and stability. According to the model, the admissible condition is derived in terms of Lyapunov‐Krasovskii stability theory, and the co‐design method of the H∞ controller and event‐triggered scheme is also presented based on the above results. The presented method emphasizes the employment of event‐triggered control to a class of singular systems with time delay. Finally, two simulation examples are provided to illustrate the effectiveness of the proposed method.

Asynchronous sampled-data consensus of singular multi-agent systems based on event-triggered strategy

ABSTRACTThis paper is concerned with sampled-data consensus for multi-agent systems with singular dynamics. It is assumed that the sampling period of each agent is independent of the other's. Based on event-triggered sampled-data transmission strategy, a distributed consensus protocol is presented. The consensus of singular multi-agent system is transformed into the stability of singular systems with multiple time-varying delays. By employing the Lyapunov-Krasovskii functional method, a sufficient condition on the consensus of multi-agent singular system is derived. Based on the obtained condition, an algorithm to design consensus controller gains is presented in terms of linear matrix inequalities. Two numerical examples are given to show the effectiveness of the proposed method.

An Alternative Admissibility Theorem for Singular Fractional Order Systems

This work is concerned with the issue of admissibility for singular fractional order systems (FOS) with the fractional order $1\leq \alpha . Firstly, an admissibility equivalence theorem is presented to establish a bridge between singular FOS and corresponding integer order systems. Then, an alternative necessary and sufficient condition for singular FOS different from existing results is developed. In this new criterion, singular matrix $E$ is included in matrix inequality, which can better deal with the issue of stabilization for singular systems with uncertainty matrix $E$ . Moreover, generalized Lyapunov equation of singular FOS is established, which is equivalent to the proposed alternative admissibility criterion. Finally, two numerical examples are presented to illustrate the effectiveness of main results in this paper.

Stochastic stabilization of singular systems with Markovian switchings

This paper studies the stochastic stabilization problem for a class of singular Markovian jump system. The aim is to determine whether or not there is a stochastic feedback controller stabilizing a given singular Markovian jump system (SMJS). A new kind of stochastic controller only in the diffusion part is proposed such that the closed-loop system has a unique solution and is almost surely exponentially admissible. New sufficient condition for the existence of such a controller is given as linear matrix inequalities (LMIs). Based on this, more extensions to transition probability matrix (TPM) with elements partially unknown and system states partially observable are developed. A numerical example is used to demonstrate the effectiveness of the proposed methods.

New result on exponential stability for singular systems with two interval time‐varying delays

This article mainly studies the problem of the exponential stability for singular systems with two interval time-varying delays. By constructing a modified Lyapunov-Krasovskii functional (LKF) and utilising a convex polyhedron method to estimate the derivative of LKF, some new delay-dependent criteria can be established in terms of linear matrix inequalities. Compared with some existing literatures, the novelties in this study are that the needed decisive variables are fewer and the obtained delay-dependent stability criteria are less conservative. Finally, two illustrative numerical examples are given to show the effectiveness of the derived results.

Dynamic soft variable structure control of singular systems

The dynamic soft variable structure control (VSC) of singular systems is discussed in this paper. The definition of soft VSC and the design of its controller modes are given. The stability of singular systems with the dynamic soft VSC is proposed. The dynamic soft variable structure controller is designed, and the concrete algorithm on the dynamic soft VSC is given. The dynamic soft VSC of singular systems which was developed for the purpose of intentionally precluding chattering, achieving high regulation rates and shortening settling times enhanced the dynamic quality of the systems. It is illustrated the feasibility and validity of the proposed strategy by a simulation example, and an outlook on its auspicious further development is presented.

Robust PD State Feedback Controller Design for Uncertain Singular Systems

This paper is concerned with the problem of robust stability and stabilization of singular systems with uncertainties in both the derivative and state matrices. By using a parameter dependent Lyapunov function, we derive the LMI-based sufficient conditions for the stabilization of the singular systems. Secondly, by solving these LMIs, a proportional plus derivative (PD) state feedback controller is designed for the closed-loop systems to be quadratically normal and quadratically stable (QNQS). Finally, the numerical example is given to show the effectiveness of the proposed theorems.

Robust D stabilization of singular systems with polytopic uncertainties

The robust D stabilization problem is considered for singular systems with polytopic uncertainties in this paper. Both the derivative matrix E and the state matrix A are with uncertainties, which were not considered before. First, with the introduction of some free matrices, a necessary and sufficient condition for the singular system to be D stable is proposed, based on which, the robust D stable problem is solved, and a sufficient condition for the closed system to be robust D stabilizable is obtained. The desired state feedback controller is given in an explicit expression. Numerical examples show the efficiency of the proposed approach.

Robust stability and stabilization for singular systems with state delay and parameter uncertainty

Considers the problems of robust stability and stabilization for uncertain continuous singular systems with state delay. The parametric uncertainty is assumed to be norm bounded. The purpose of the robust stability problem is to give conditions such that the uncertain singular system is regular, impulse free, and stable for all admissible uncertainties, while the purpose of the robust stabilization is to design a state feedback control law such that the resulting closed-loop system is robustly stable. These problems are solved via the notions of generalized quadratic stability and generalized quadratic stabilization, respectively. Necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are derived. A strict linear matrix inequality (LMI) design approach is developed. An explicit expression for the desired robust state feedback control law is also given. Finally, a numerical example is provided to demonstrate the application of the proposed method.

Bifurcation on stability of singular systems with delay

In this paper, the general class of singular systems with delay and second order linear constant coefficients singular systems with delay, is considered. First, for singular systems with delay, new definitions of stability are presented, and general sufficient stability conditions and instability conditions are derived. Secondly, these results are applied to the analysis of stability and instability of second-order linear constant coefficients singular systems with delay, the location of a possible bifurcation is discovered.

Structural Stability for Singular Systems a Quantitative Approach

This paper studies the structural stability for singular systems. The problem is solved via the matrix perturbation analysis method. Allowed perturbation regions for structural stability are given.