Relaxed Stability Criteria for Time-Delay Systems:A Novel Quadratic Function Convex Approximation Approach

This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By introducing two adjustable parameters and two free variables,a novel convex function greater than or equal to the quadratic function is constructed,regardless of the sign of the coefficient in the quadratic term.The developed lemma can also be degenerated into the existing quadratic function negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular values.Moreover,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality.As a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems.Finally,the superiority of our results is illustrated through three numerical examples.

Optimal disturbances rejection control for singularly perturbed systems with time-delay

The optimal control design for singularly perturbed time-delay systems affected by external distur-bances is considered.Based on the decomposition theory of singular perturbation,the system is decom-posed into a fast subsystem without time-delay and a slow time-delay subsystem with disturbances.Theoptimal disturbances rejection control law of the slow subsystem is obtained by using the successive ap-proximation approach(SAA)and feedforward compensation method.Further,the feedforward and feed-back composite control(FFCC)law for the original problem is developed.The FFCC law consists of lin-ear analytic terms and a time-delay compensation term which is the limit of the solution sequence of theadjoint vector equations.A disturbance observer is introduced to make the FFCC law physically realiz-able.Numerical examples show that the proposed algorithm is effective.

Hierarchical Dispatch Method for Integrated Heat and Power Systems Based on a Feasible Region of Boundary Variables

Fully utilizing the flexibility provided by a district heating system(DHS)can promote wind power accommodation for an electric power system(EPS).However,for privacy or communication reasons,existing power and heat dispatch methods are not suitable for practical application.In this paper,a general math formulation of the hierarchical dispatch method is proposed to coordinate EPS and DHS operators based on the feasible region of boundary variables(FRBV),and a method based on the simplicial approximation approach is proposed to obtain a conservative FRBV approximation of a DHS.A simulation based on a real 41-node DHS is constructed to determine the factors that may impact the boundaries of the FRBV,and then the performance of the simplicial approximation approach is displayed by visualizing the approximation process for the FRBV,and finally three dispatch methods are compared to show the advantages of the proposed hierarchical dispatch method.