Synthesis of time-varying bandwidth filters based on all-pole LTI prototypes

This paper presents a systematic procedure for synthesizing a class of time-varying bandwidth (TVB) filter using a parallel D-eigenvalue concept and a stability criterion for linear time varying (LTV) systems. Time-varying frequency response of the TVB filter is analyzed and a computable procedure is used to obtain “time-varying Bode plots”. Comparisons are made with LTI filters with or without limiter to demonstrate the advantages of the TVB filter. While the procedure is presented for nth-order single-input-single-out lowpass filters based on all-pole LTI prototypes, extension of the results to more general cases are addressed. Application for tracking command shaping filters, implementation of pseudo-differentiators, pseudo-inverse of nonlinear dynamics and nonlinear asymptotic state observers are also discussed