Observer-based strict positive real (SPR) feedback control system design

This paper presents theory for stability analysis and design for a class of observer-based feedback control systems. Relaxation of the controllability and observability conditions imposed in the Yakubovich-Kalman-Popov (YKP) lemma can be made for a class of nonlinear systems described by a linear time-invariant system (LTI) with a feedback-connected cone-bounded nonlinear element. It is shown how a circle-criterion approach can be used to design an observer-based state feedback control which yields a closed-loop system with specified robustness characteristics. The approach is relevant for design with preservation of stability when a cone-bounded nonlinearity is introduced in the feedback loop. Important applications are to be found in nonlinear control with high robustness requirements.

[1]  S. Joshi,et al.  Strictly positive real transfer functions revisited , 1990 .

[2]  Rolf Johansson,et al.  Extension of the Yakubovich-Kalman-Popov Lemma for Stability Analysis of Dynamic Output Feedback Systems , 1999 .

[3]  T. Başar.  Absolute Stability of Nonlinear Systems of Automatic Control , 2001 .

[4]  Anders Robertsson,et al.  Observer-Based SPR Feedback Control System Design , 2002 .

[5]  S. Lefschetz.  Stability of nonlinear control systems , 1966 .

[6]  S. Glad.  On the gain margin of nonlinear and optimal regulators , 1984, 1982 21st IEEE Conference on Decision and Control.

[7]  Vasile Mihai Popov,et al.  Hyperstability of Control Systems , 1973 .

[8]  P. C. Parks,et al.  A. M. Lyapunov's stability theory—100 years on , 1992 .

[9]  K. Meyer.  On the Existence of Lyapunov Function for the Problem of Lur’e , 1965 .

[10]  K. Narendra,et al.  Frequency Domain Criteria for Absolute Stability , 1973 .

[11]  I. Bar-Kana.  Parallel feedforward and simplified adaptive control , 1987 .

[12]  R. E. Kalman,et al.  When Is a Linear Control System Optimal , 1964 .

[13]  G. Stein,et al.  Robustness with observers , 1978, 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes.

[14]  David J. Hill,et al.  Stability results for nonlinear feedback systems , 1977, Autom..

[15]  J. Willems,et al.  Synthesis of state feedback control laws with a specified gain and phase margin , 1980 .

[16]  R. Kálmán.  LYAPUNOV FUNCTIONS FOR THE PROBLEM OF LUR'E IN AUTOMATIC CONTROL. , 1963, Proceedings of the National Academy of Sciences of the United States of America.

[17]  John C. Doyle,et al.  Guaranteed margins for LQG regulators , 1978 .

[18]  G. Zames.  On the input-output stability of time-varying nonlinear feedback systems--Part II: Conditions involving circles in the frequency plane and sector nonlinearities , 1966 .

[19]  J. Willems.  Dissipative dynamical systems part I: General theory , 1972 .

[20]  P. Kokotovic,et al.  A positive real condition for global stabilization of nonlinear systems , 1989 .