Stability analysis and design of uniform ultimate boundedness control for a class of nonlinear switched difference systems

This paper addresses the problems of stability analysis and synthesis of uniform ultimate boundedness (UUB) control for a class of nonlinear switched difference systems. This kind of discrete-time systems could be regarded as the digitization systems induced from the corresponding continuous-time switched system in virtue of the numerical integration approach, such as Euler or Runge-Kutta method. A sufficient stability condition in terms of linear inequalities is presented to ensure that for prescribed digitalized steps the switched difference system is stable for an arbitrary switching signal. Moreover, a constructive algorithm based on the modified Gaussian elimination procedure is given to find the solutions to the linear inequalities. Finally, continuous state feedback control methods are developed to guarantee uniform ultimate boundedness of the switched systems with nonlinear and time-varying parameter uncertainties and unknown input disturbances. A numerical example illustrates the effectiveness of the proposed approach.