Yong-Qing Liu

Basic Theory of Singular Systems of Linear Differential Difference Equations 1

Abstract This paper discusses singular systems of constant coefficient linear differential difference equations with delay, there are many cases of this class of systems because of different coefficients, in some cases, there exists a unique solution, and in some cases, there exist infinite solutions, under some initial condition and consistency condition; In some cases, there is no solution. Also there are many types of equation included in this class of systems, such as, neutral differential difference equation, composite systems of differential algebraic equation with delay, and so on. Above all, it is very complicated. This paper analyzes the existence, uniqueness of solutions, establishes the basic theory of solutions.

Fundamental principle and synthesis of variable structure control for nonlinear neutral control systems with time-delays*

Abstract This paper investigates the practicality problem of the equivalent control method for nonlinear neutral type variable structure control system (VSCS) with time-delays. Existence of the sliding mode for the system is given, and the conditions under which the sliding process has nothing to do with the external disturbance and parameter perturbation are obtained. At last, the synthetical method of the VSCS is provided and illustrated by an example of chemical process.

Robust Stability of Impulsive Large-Scale Time-Varying Interval Delay Systems

Abstract The problem of robust stability for impulsive large scale time-varying interval dynamical systems with delays which has not been studied up to now is introduced and studied. Some explicit criteria of exponential robust stability in the large for such systems are established based on vector comparison theorem and the techniques of matrices and inequalities.

Decentralized exponential stabilization of deterministic and stochastic large scale systems: a unified approach

A unified approach to decentralized exponential stabilization for both deterministic and stochastic large-scale interconnected systems is proposed. An algorithm is given for designing local state feedback controllers to stabilize the large scale-systems. Two examples are given to show the applicability of the approach.<<ETX>>

The generalized fourier transform theorem and its application to singular distributed parameter systems

ABSTRACT Concepts of the generalized left inverse, the generalized Fourier transform and the square root of matrix are defined in this the paper. Meanwhile, this paper deals with singular distributed parameter systems described by coupled partial differential equations with singular matrix coefficients. As to the singular distributed parameter systems, the initial-value problem are considered on the basis of the generalized Fourier tranform theorem. The solution of the systems is obtained the method presented here the possibility of determining acceptable initial-value conditions.

Linear and Nonlinear Local State Feedback for Decentralized Stabilization of Stochastic Large Scale Systems

Abstract By introducing both linear and nonlinear local state feedback controllers, criteria are established for the decentralized stabilization of time-invariant and time-varying stochastic large scale systems. These criteria are given by the hypotheses for diffusion coefficients and expressed by the matrix Riccati equations. In time-invariant case, the hypotheses for matrix Riccati equations can be ensured by the conditions of stabilizability and observability of the isolated stochastic subsystems.

Variable structure control of linear delayed large-scale systems

Abstract This paper presents the design of decontralized variable structure controllers in the linear large scale control systems with time-delays, including some design methods of control systems under certain given conditions as well as local decentralized controllers and the multilayer decentralized variable structure controllers by means of the concept and method of approaching rates.

Variable structure control of completely retarded stochastic systems

Abstract In this paper, variable structure control of completely retarded Ito stochatic systems is investigated, the variable structure control law is constructed, the achievability and sub-achievability of the sliding mode motions are defined, the achievability and stability of the sliding mode are investigated with the stochastic analysis method and delay differential inequalities, and a design example is given to show the method of this paper.

Decentralized Stabilization of Large-Scale Stochastic Systems with Delay Uncertain Interconnection 1

Abstract This paper is devoted to the decentralized stabilization of large-scale stochastic systems of Ito type with delay uncertain interconnection by Lyapunov functional. Criteria are established for the large-scale stochastic systems to be stabilized by decentralized controllers. An associated algorithm named SLC is given to obtain the decentralized controllers. The criteria and algorithm can be applied to deterministic large-scale systems as a special case.

Neutral Volterra Nonlinear Singular Systems with Boundary Value Constraint

Abstract In this paper, we discuss well-posed boundary conditions and expression of solutions of nonhomogeneous singular systems with boundary value constraint (BVC). And then neutral Volterra nonlinear singular systems with BVC are considered by employing the contraction principle and the property of singular systems. Finally several corollaries are included. Our results will extend the results for normal systems (i.e. E is nonsingular) to singular systems. These results are fundamental to the development of the theory on nonlinear singular systems with BVC.