Stability of a General Type of Pulse-Width-Modulated Feedback System

The stability of pulse-widtli-modulated control systems has been an active area of research since the early 1960's. A variety of graphical and analytical approaches to the problem have appeared in the literature. 1 - 4 Aside from the approximate methods, the main contribution of the early 19(i0's to exact stability criteria was in the application of Lyapunov's direct method. 5 ' 6 As is often the case, this approach yields conservative results and does not easily lend itself to system compensation. Input-output stability via functional analytic techniques was reported in Skoog 7 and Skoog and Blankenship, 8 where conditions for the L boundedness and continuity of the system operator are derived for PWM systems (considered there to belong to a larger class of pulse-modulated systems, i.e., that class of modulators for which the input is sampled). One drawback to the above type of criteria is the lack of a simple geometric interpretation; e.g., a Popovtype condition. In Skoog 7 a circle criterion is derived for P W M systems, operating in the "quasi-linear" mode; that is, where the modulator does not saturate. In its exact form, however, the above condition is rather 1811