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A mathematical fitting modeling method based on Ant Colony Algorithm and which can effectively reflect the intrinsic mechanism eigenvalue of ECG is studied. The measured ECG signals are taken as the research object, fitting methods are used to obtain multiple characteristic parameters, ITAE is used as the evaluation criteria, and then the parameters are acquired through the ant colony algorithm, in the end, the model of calculated parameters for ECG is established, this fitting way can not only enrich the date of ECG in QRS, but also provide effective data for further research such as magnetoelectricity inversion calculation, expanding the mathematical fitting method for analyzing discrete signals such as electrophysiology.

An adaptive notch filter is presented to estimate the fundamental frequency and measure both harmonics and interharmonics of an almost periodic signal with unknown time-variant fundamental frequency, which has the robustness that the convergence speed is determined by neither amplitude nor frequency of fundamental component. The algorithm forms a one-dimensional slow adaptive integral manifold whose existence and stability are proved by averaging method and Lyapunov stability theorem. The local exponential stability and the ultimate boundedness of fundamental frequency estimation are proved. The local exponential stability makes sure that the fundamental frequency, the harmonic and interharmonic components can be all fast tracked. The principle for adjusting the parameters with their influences on transient and steady-state performance is investigated and decreasing parameters can improve noise characteristic. The validity is verified by simulation results.

A nonlinear system being composed of multiadaptive notch filters in parallel is introduced to track the sinusoidal components of an almost periodic signal and estimate their frequencies and amplitudes. An almost periodic nonlinear dynamic system for estimation of frequencies is achieved after the existence of a slow integral manifold is proved and results in a nonlinear autonomous system with averaging method employed. Three types of local stability of the autonomous system, the exponential stability in isolated equilibrium point and the semistability on center manifold and the ultimate boundedness under unknown periodic disturbance, are respectively investigated. The transient performance is affected by frequency adaptive gain independent of bandwidth parameter. The validity of the proposed algorithm is verified by simulation results.

The robust control for a class of distributed parameter switched systems with time-delay is studied. The sufficient condition for the existence of the hybrid state feedback robust controller for the closed-loop switched systems is obtained based on Green formula and Lyapunov function method. Using the linear matrix inequality (LMI) approach, the design of the robust controller is converted into finding feasible solutions of a group of LMIs, which can be efficiently carried out using Matlab LMI toolbox. Simultaneously, the method to reduce the conservativeness of the design for the robust control system is also investigated. Finally, a numerical example is presented to show the validity of the proposed design method.