on the global practical stabilization of discrete-time switched affine systems: application to switching power converters

This paper presents new sufficient conditions as a set of bilinearmatrix inequalities (bmis) for the global practical stabilization ofdiscrete-time switched affine systems. the main contribution is onproposing the stability conditions based on a common quadraticlyapunov function that can be used to stabilize the discrete-timeswitched affine systems around a desired equilibrium point for whichit is not required to find any schur stable convex combination ofoperating modes as a pre-processing stage, that needs specialalgorithms and is an np-hard problem. the result is that theexisting two-stage stabilization methods based on a pre-calculationof a schur stable convex combination of operating modes aresimplified to a single-stage method by which a high degree ofapplicability is obtained. the proposed stability conditions aredeveloped in a way the size of the convergence ellipsoid isminimized. moreover, it is not required the equilibrium point,around which the invariant set of attraction is constructed, beinside a predetermined set of attainable equilibrium points. thesatisfactory operation of the proposed stability conditions isillustrated by an academic example and application onvarious dc-dc converters.