First order reset elements and the Clegg integrator revisited

• Published in: 2005 American Control Conference pp. 563 - 568 vol. 1
• Main Authors: Zaccarian, L., Nesic, D., Teel, A.R.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 2005
• Subjects: Asymptotic stability; Australia; Control system synthesis; Control systems; Frequency domain analysis; Linear matrix inequalities; Lyapunov method; Robustness; Stability analysis; Sufficient conditions
• ISBN: 0780390989; 9780780390980; 9780780390997; 0780390997
• ISSN: 0743-1619
• DOI: 10.1109/ACC.2005.1470016

We revisit a class of reset control systems containing first order reset elements (FORE) and Clegg integrators and propose a new class of models for these systems. The proposed model generalizes the models available in the literature and we illustrate, using the Clegg integrator, that it is more appropriate for describing the behavior of reset systems. Then, we state computable sufficient conditions for L/sub 2/ stability of the new class of models. Our results are based on LMIs and they exploit quadratic and piecewise quadratic Lyapunov functions. Finally, a result on stabilization of linear minimum phase systems with relative degree one using high gain FOREs is stated. We present two examples to illustrate our results. In particular, we show that for some systems a FORE can achieve lower L/sub 2/ gain than the underlying linear controller without resets.