Interval Criterion of Robust Stability for Nonlinear System and Its Application to Flight Control

Robust stability for a series of nonlinear systems is presented in this paper. Through different region descriptions, the problem of stability for a complex nonlinear system is transformed into ones of the robust stabilities of several linear time-invariant systems. To get useful robust stability conditions, an expression for interval system is given, and the relationship between the internal stability and low- or supper-bound stability of interval systems is discussal. Thus, the polynomial matrix inequality for the determination of system robust stability is developed. Based on the equivalency transformation of the inequality, the solvable condition of the inequality is obtained. By means of the condition, robust stability theorem for interval systems is presented and a new design method of feedback control for nonlinear system is achieved. Applications to flight controller design show that the new method is efficient for uncertain system design.