This note concerns the problem of the robust stability of a linear system with a time-varying delay and polytopic-type uncertainties. In order to construct a parameter-dependent Lyapunov functional for the system, we first devised a new method of dealing with a time-delay system without uncertainties. In this method, the derivative terms of the state, which is in the derivative of the Lyapunov functional, are retained and some free weighting matrices are used to express the relationships among the system variables, and among the terms in the Leibniz-Newton formula. As a result, the Lyapunov matrices are not involved in any product terms of the system matrices in the derivative of the Lyapunov functional. This method is then easily extended to a system with polytopic-type uncertainties. Numerical examples demonstrate the validity of the proposed criteria.

This paper presents necessary and sufficient conditions for the existence of a Lyapunov function in the Lur'e form that guarantees the absolute stability of a Lur'e control system with multiple nonlinearities. It simplifies the existence problem to one of solving a set of linear matrix inequalities (LMIs). If these inequalities are feasible, the free parameters in the Lyapunov function, such as the positive definite matrix and the coefficients of the integral terms,are given by the solution of the LMIs. Otherwise, there does not exist any Lyapunov function in the Lur'e form. Necessary and sufficient conditions are also obtained for the robust absolute stability of time-varying structured uncertain systems.

This note concerns delay-dependent robust stability criteria and a design method for stabilizing neutral systems with time-varying structured uncertainties. A new way of deriving such criteria is presented that combines the parameterized model transformation method with a method that takes the relationships between the terms in the Leibniz-Newton formula into account. The relationships are expressed as free weighting matrices obtained by solving linear matrix inequalities. Moreover, the stability criteria are also used to design a stabilizing state-feedbackcontr oller. Numerical examples illustrate the effectiveness of the method and the improvement over some existing methods.

This paper concerns a real-world application of an expert system to the automation of a zinc hydrometallurgy plant. The leaching process in zinc hydrometallurgy involves dissolving zinc-bearing material in dilute sulfuric acid to form a zinc sulfate solution. The key problems are to determine and track the optimal pHs of the overflows of the neutral and acid leaches, and to ensure the safe running of the process. This paper describes an expert control and fault diagnosis scheme that solves those problems. The expert control is based on a combination of steady-state mathematical models and rule models, and the fault diagnosis employs rule models with certainty factors and a Bayes representation. A real-world application of this scheme showed that it not only improved the control performance, but also correctly diagnosed faults.

(t)=Ax(t)+A1x(t −h1(t))+B1u(t)+B2u(t −h2(t)). In this paper, a new integral inequality for quadratic terms is first established. Then, it is used to obtain a new state- and input-delay-dependent criterion that ensures the stability of the closed-loop system with a memoryless state feedback controller. Finally, some numerical examples are presented to demonstrate that control systems designed based onthe criterionare effective, eventhough neither (A,B1) nor (A+A1,B1) is stabilizable.