This paper is concerned with the stability and disturbance attenuation properties of switched linear system with dwell time constraint. A novel time-scheduled Lyapunov function is introduced to deal with the problems studied in this paper. To numerically check the existence of such time-scheduled Lyapunov function, the discretized Lyapunov function technique usually used in time-delay system is developed in the context of switched system in continuous-time cases. Based on discretized Lyapunov function, sufficient conditions ensuring dwell-time constrained switched system global uniformly asymptotically stable are established, then the disturbance attenuation properties in the sense ofL2gain are studied. The main advantage of discretized Lyapunov function approach is that the derived sufficient conditions are convex in subsystem matrices, which makes the analysis results easily used and generalized. Thus, theH∞control synthesis problem is considered. On the basis of analysis results in hand, the control synthesis procedures including both controller and switching law design are unified into one-step method which explicitly facilitates the control synthesis process. Several numerical examples are provided to illustrate the results within our paper.
The research on scroll profiles theory at present mainly is aiming at the single profile and its amelioration or parameter optimization, not aiming at the natural characteristic of the profiles equation of scroll profiles itself. Thus, the intrinsic differential equation bearing on arc-length and tangent direction angle was studied. Using the inherent differential equation and general functional theory, the conversion ideas between the expression of intrinsic differential equation and the expression in Cartesian coordinate was studied, and the condition of involutes characteristic was presented. The detailed analysis of four typical scroll profiles was given. According to the four typical scroll profiles and based on the method of Taylor series, the unified formation of general functional integration scroll profiles was established, which perfected general theory of scroll profiles increasingly. The envelope method to seek conjugation engagement profiles was studied. The unified general functional equation of scroll profiles represented the admissible function scrolls and the conjugation engagement characteristic of which was studied. The engagement condition of conjugation scroll profiles and the expression in Cartesian coordinate of conjugation scroll profiles of general functional integration scroll profiles were educed. Therefore, the restriction of inherent characteristics of single scroll profiles model is broken through. Solid modeling and machine tool path simulation can bridge the gap between design and manufacture which is essential for the design and manufacture of scroll compressors. With this method a perfect solid model can be achieved, which leads to an optimal design in terms of quality, delivery time and cost. The presentation of unified formation of general functional integration scroll profiles represents foundation factor of instinct characteristics of scroll profiles, which widens the design method of scroll compressor for automobile air conditioning. automobile air conditioning, scroll compressor profiles, integrated design, expression transform, application analysis Citation:Wang L C, Du L, Zhang X M, et al. A study on integrated design conjugation profiles application analysis of scroll profiles for automobile air conditioning.
Using add-order method to translate the problem of generalized synchronization of different orders of chaotic systems into the synchronization of systems of identical order. Based on Lyapunov stability theory and adaptive control method, we give the expression of adaptive controller and the updating rule of parameters, then achieve generalized synchronization of different order of chaotic systems with unknown parameters and enable the estimation of the parameters of the drive and the response systems. This method has been applied to solve the generalized synchronization problem of hyperchaotic Lü system, Lorenz system, generalized Lorenz system, and Liu system with unknown parameters. It is proved theoretically that this method is feasible. Numerical simulations show the effectiveness of the adaptive control technique.
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