Quadratic Performance Analysis of Switched Affine Time–Varying Systems

We analyze quadratic performance for switched systems which are composed of a finite set of affine time-varying subsystems, where both subsystem matrices and affine vectors are switched, and no single subsystem has desired quadratic performance. The quadratic performance indexes we deal with include stability, tracking and L2 gain. We show that if a linear convex combination of subsystem matrices is uniformly Hurwitz and another convex combination of affine vectors is zero, then we can design a state-dependent switching law (state feedback) and an output-dependent switching law (output feedback) such that the entire switched affine system is quadratically stable at the origin. In the case where the convex combination of affine vectors is nonzero, we show that the tracking control problem can be posed and solved using a similar switching strategy. Finally, we consider the L2gain analysis problem for the switched affine time-varying systems under state feedback.

An Application of Modified Predictor-Corrector Method

The explicit numerical integration method, introduced and proposed in the paper given by Chiou and Wu [1], is further developed. The method is based on the relationship that m-step Adams-Moulton method is linear convex combination of the (m − 1)-step Adams-Moulton and m-step Adams-Bashforth method with a fixed weighting coefficients. The general form taken from Chiou and Wu [1] is used to evaluate the recurrence expressions using the different number of previous mesh points. The explicit expressions are given for modified 3-step predictor-corrector method. The numerical algorithms are given for first and second-order nonlinear initial value problems and for system of ordinary differential equations. Some numerical examples, for different kind of problems, are used to demonstrate the efficiency and the accuracy of the proposed numerical method. The calculated numerical solutions show superiority of presented modified predictor-corrector method to standard Adams-Bashforth-Moulton predictor-corrector method.