Linear Time-varying Singular Systems Research Articles

Parameterization technique for solving variational formulation of index three linear time-varying singular control systems

This paper deals with finding an approximate solution to an index three time-varying linear differential algebraic control equations based on the theory of variational formulation. The critical points of the formulated variational functional subject to the differential- algebraic equation with the class of consistent initial conditions are shown to be the solution of the proposed index-three DAEs with control problem (singular control systems) and vise- versa. The given variational problem is also transformed from indirect method into direct method using generalized Ritz bases technique. From the numerical illustrations results, the efficiency and very good accuracy as well as the simplicity of the present approach are obtained.

Cooperative output regulation of singular multi-agent systems under adaptive distributed protocol and general entirety method

This paper investigates the cooperative output regulation problem of heterogeneous linear multi-agent systems under singular dynamics and adaptive distributed protocol. Considering the followers do not know the matrix information of the leader, two novel adaptive distributed protocols are developed based on the state and measurement output. Then, as the technology basis of the cooperative output regulation strategy of the singular multi-agent systems considered in this paper, some stability analysis results of linear time-varying singular systems are proved. Next, sufficient conditions are established to solve the cooperative output regulation problem of heterogeneous singular multi-agent systems with the adaptive distributed protocols designed in this paper. The general entirety method is proposed, which avoids the design of standard reduction transformation matrices, the calculation of model reduction and the impulse-free hypothesis in the standard reduction method. Finally, numerical results are provided to demonstrate the feasibility and effectiveness of the proposed techniques.

On the strong observability in linear time-varying singular systems

In this article the strong observability conditions, necessary and sufficient conditions originally stated for the state reconstruction of linear systems with unknown inputs, are extended to the class of linear time-varying singular systems. This novel local (in a time interval of interest) conditions are given under a constant rank assumption. A method to reconstruct the state in finite time in linear time-varying singular systems despite the presence of unknown inputs is presented. The proposed observer consists of two parts, one part that ensures the asymptotic convergence of the estimation errors to a bounded region around the origin and another one that ensures the finite-time convergence of the state estimates to their actual values.

Exponential Stability and Robust Stability for Linear Time-Varying Singular Systems of Second Order Difference Equations

In this paper, solvability, stability, and robust stability of linear time-varying singular systems of second order difference equations are studied. The leading coefficient is allowed to be singul...

English

This paper considers the finite-time stability of linear time-varying singular impulsive systems. A lemma which states an important inequality was first established. Then some sufficient conditions for the systems to be finite-time stable were derived. The proposed results remove some restrictions of the existing methods and thus can be applied to more general systems. Finally, a numerical example was presented to illustrate the proposed approaches.   Key words: Singular impulsive systems, finite-time stability, comparison principle.

Finite-time stability of linear time-varying singular impulsive systems

In this study, the problem of finite-time stability of linear time-varying singular systems with impulses at fixed times is addressed. Sufficient conditions for linear singular impulsive systems to be finite-time stable are proposed in terms of a set of coupled matrix inequalities. Two numerical examples are given to illustrate the effectiveness of the obtained theoretical results.

On Controllability and Observability of Linear Time-varying Singular Systems

摘要: 讨论了线性时变系统和线性时变广义系统的两个基本问题, 得到了两种判定时变系统能控性与能观性的必要条件, 该判定条件只依赖于系统矩阵A(t)和输入矩阵B(t), 不必计算系统的系统状态转移矩阵, 使得判别时变系统能控性与能观性易于实现. 说明了本文结论是线性定常系统相应结论的自然扩展. 对进一步深入研究时变系统和时变广义系统具有实际启发作用. 关键词: 时变系统 / 广义系统 / 能控性 / 状态转移矩阵

Finite-time stability of linear time-varying singular systems with impulsive effects

In this paper, we introduce a new concept of finite-time stability of linear time-varying singular systems with impulses at fixed times, and present new results for the above-mentioned class of system in the form of sufficient conditions. A sufficient condition is given in terms of matrix inequalities, which gives the opportunity of fitting the finite-time control problem in the general framework via impulsive control. A numerical example is presented to illustrate the efficiency of the proposed result.

Impulse Analysis of Linear Time-Varying Singular Systems

Impulsive part of solution to initial value problem of linear time-varying singular systems is given explicitly. Impulse observability and impulse controllability for the systems are redefined

On linear quadratic optimal control of linear time-varying singular systems

Linear time-varying singular systems are treated in this paper. We focus on systems with constant-rank E matrices. It is shown that the existence of state feedback for impulse elimination is both sufficient and necessary for the existence of linear-quadratic optimal control. Also optimal control exists if and only if the corresponding fast subsystem is impulse-controllable. The results obtained are extensions of the existing time-invariant theory.

Disturbance decoupling of linear time-varying singular systems

The problem of disturbance decoupling by state feedback is defined for a linear time-varying singular system. It is required that the closed-loop system has a unique impulse-free solution and its output is not affected by disturbances. An algorithm, namely disturbance decoupling algorithm, is proposed. It is proved that the feasibility of the disturbance decoupling algorithm is invariant under any regular feedback control law. Based on the disturbance algorithm, a constructive method is provided to design a disturbance decoupling feedback control law. Sufficient conditions for the solvability of the disturbance decoupling problem are derived. It is proved that one of the sufficient conditions is also necessary provided that other conditions are satisfied.

Impulse observability and impulse controllability of linear time-varying singular systems

Impulse controllability and impulse observability of linear time-varying singular systems in a standard canonical form are examined. We focus on the fast subsystems with constant-rank N matrices. Sufficient and necessary conditions are derived and presented directly in terms of system parameters. Conditions obtained for these two properties are algebraically dual to each other.

Input-output block decoupling of linear time-varying singular systems

The input-output block decoupling problem by state feedback is studied for linear time-varying singular systems. First, an algorithm, the regularization algorithm, is developed such that the system can be made by state feedback to have a unique impulse-free solution. Second, another algorithm, the block decoupling algorithm, is proposed, which provides sufficient conditions for the solvability of the input-output block decoupling problem. Then, a decoupling feedback law is constructed such that the corresponding closed-loop system is regular, impulse-free, and noninteractive. Finally, an example is given to illustrate the applicability of the algorithms.

Input-output decoupling of linear time-varying singular systems

The problem of input-output decoupling by state feedback is considered for linear time-varying singular systems. Assumptions are introduced, and an algorithm is developed such that the system can be expressed in a simple normal form. A time-varying feedback law is then constructed which ensures, under appropriate conditions, that the closed-loop system is regular, impulse-free, and noninteractive.

An input-output representation for implicit linear time-varying systems

The need to describe the input-output behavior of implicit differential systems arises in many contexts, including computer-aided modeling and the analysis of dynamical control systems. For a linear time-varying singular control system with real analytic coefficients in state space form, we produce an external (input-output) description of the system behavior in the form of a set of higher order differential equations in the inputs and outputs. The component of the state vector that affects the input-output relation is identified by a projection matrix which is computable from the original system coefficient matrices. The resulting input-output equations involve redundancy, but the input-output representation is obtained using computations on the original system without applying coordinate transformations.

An input-output representation for implicit linear time-varying systems

The need to describe the input-output behavior of implicit differential systems arises in many contexts, including computer-aided modeling and the analysis of dynamical control systems. For a linear time-varying singular control system with real analytic coefficients in state space form, we produce an external (input-output) description of the system behavior in the form of a set of higher order differential equations in the inputs and outputs. The component of the state vector that affects the input-output relation is identified by a projection matrix which is computable from the original system coefficient matrices. The resulting input-output equations involve redundancy, but the input-output representation is obtained using computations on the original system without applying coordinate transformations.

Uniform Regularity and Decomposition for Linear Time Varying Singular System in Rational Fraction Domain

In this paper, linear time-varying singular systems in RATIONAL FRACTION DOMAIN (RFD) have been studied by using the UMR transform. The LTVSS in RFD can be put into a standard decomposition which is quite similar to that of a time-invariant case. The calculating method of the standard form is also proposed. In the third part the three examples also explained that the basic definitions of uniformly regular and the assumption of constant rank are necessary. The timevarying fast subsystems (or restricted equations), which are related to the input u(t), has a time varying coefficients B2 (t) ∈ RFD

State feedback impulse elimination of linear time-varying singular systems

Linear time-varying singular systems E(t) x ̇ = A(t)x + B(t)u are treated. A necessary and sufficient condition for the existence of linear state feedback to eliminate impulsive behavior is derived. The condition obtained is a natural extension of existing time-invariant theory.

The Output-Nulling Space, Projected Dynamics, and System Decomposition for Linear Time-Varying Singular Systems

A decomposition of a given linear time-varying singular control system is developed by defining the output-nulling space with respect to a given output structure. Relevant subspaces and the dynamics on them are described by computable projection operators obtained from information in the system's derivative array. The relevant projectors are generated as solutions of a homogeneous linear matrix-differential equation. An algorithm for obtaining the system decomposition is outlined in a pointwise manner.

Note on single-term Walsh series method for singular systems

By considering linear time-varying singular systems in discrete time it is shown that the single-term Walsh series technique is not applicable to singular systems of index three.