Stability analysis of a hypersonic vehicle controlled by the characteristic model based adaptive controller

The closed loop attitude stability of a hypersonic vehicle controlled by the characteristic model-based all-coefficient adaptive controller is studied in this paper,and an algorithm based on the computation of induced matrix 1-norm or ∞-norm is proposed.First of all,the Taylor series expansion is applied to discretize the inputoutput description of the attitude dynamics of the vehicle.The obtained difference equations have the same structure as characteristic model;thus the intervals which contain all possible values of certain characteristic model parameters are obtained.When the linear feedback controller is used in the feedback loop,with some conservation,the closed loop system is viewed as a class of interval time-varying systems defined by a number of free time-varying parameters.These free parameters take values from predefined intervals.The sufficient and necessary condition for the stability of this class of system is given.Finally,a sufficient condition for the stability of hypersonic vehicle attitude control loop is proposed and demonstration example is presented.The method proposed checks up the stability of the closed loop system by evaluating a finite number of matrix norms,and overcomes the difficulties brought by the time-varying nature of the characteristic model and parameter estimation.