Local Stabilizability of Linear Systems with PWM Control Inputs

This paper deals with analysis of linear control systems whose control inputs are given by pulse-width-modulation (PWM) based on binary or ternary values. The analysis is carried out for the corresponding discretized systems whose control inputs are duty ratios given at sampling instants. In particular, we investigate controllability and stabilizability of the discretized systems and its relation to that of the underlying continuous time systems. The obtained conditions are similar to those of the discretization based on the zero order hold. Moreover, we clarify the relationship between the existence of a fixed point for the discretized nonlinear system and an equilibrium point for the original continuous linear systems in the binary input case. Moreover, the connection between exponential stability of the discretized and the original systems are also discussed in the ternary input case