Disturbance Attenuation for A Class of Uncertain Polynomial Discrete-time Systems: An Integrator Approach

This paper investigates the problem of disturbance attenuation for a class of uncertain polynomial discrete-time systems with an H-infinity performance. In general, this is a difficult problem because it cannot be formulated as a convex problem. This is because the Lyapunov function and the control input is not jointly convex. Hence it cannot be solved by a semidefinite programming (SDP). In this paper, a novel approach is proposed, where an integrator is introduced into the controller structures so that a convex solution can be obtained. Furthermore, based on the sum of squares approach, sufficient conditions for the existence of a proposed nonlinear feedback controller with the integrator for a polynomial discrete-time system are given in terms of solvability of polynomial matrix inequalities (PMIs). These inequalities are then be solved by the recently developed SOS solvers. The validity of the proposed method is confirmed through a tunnel diode circuit.