Global stabilization and L2 disturbance attenuation for linear systems with bounded controls

This paper presents a technique for obtaining a bounded continuous feedback control function such that the closed-loop system is globally asymptotically stable and satisfies an L2 to L2 disturbance attenuation condition in a neighborhood of the origin. The proposed control is a linear-like feedback law with state-dependent gains.

[1]  Mario Sznaier.  A Mixed $l_{\infty}/{\cal H}_{\infty}$ Optimization Approach to Robust Controller Design , 1995 .

[2]  Andrew R. Teel,et al.  Simultaneous L p -stabilization and internal stabilization of linear systems subject to input saturation—state feedback case , 1995 .

[3]  Eduardo D. Sontag,et al.  On the continuity and incremental‐gain properties of certain saturated linear feedback loops , 1995 .

[4]  R. Suárez,et al.  Linear systems with bounded inputs : global stabilization with eigenvalue placement , 1997 .

[5]  B. G. Romanchuk.  On the computation of the induced /spl Lscr//sub 2/ norm of single input linear systems with saturation , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[6]  M. Sznaier,et al.  Robust control of constrained systems via convex optimization , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[7]  Eduardo D. Sontag,et al.  On the continuity and incremental-gain properties of certain saturated linear feedback loops , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[8]  J. Alvarez,et al.  Stabilization of linear controllable systems by means of bounded continuous nonlinear feedback control , 1994 .

[9]  Jose Alvarez-Ramirez,et al.  Semiglobal stabilization of multi-input linear systems with saturated linear state feedback , 1994 .

[10]  Mario Sznaier.  Mixed l 1 / H ∞ controllers for SISO discrete time systems , 1994 .

[11]  A. Teel.  Semi-global stabilizability of linear null controllable systems with input nonlinearities , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[12]  Athanasios Sideris,et al.  H∞ optimization with time-domain constraints , 1994, IEEE Trans. Autom. Control..

[13]  Sophie Tarbouriech,et al.  Continuous-time saturated state feedback regulators: theory and design , 1994 .

[14]  J. W. Helton,et al.  Piecewise Riccati equations and the bounded real lemma , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[15]  Eduardo D. Sontag,et al.  A general result on the stabilization of linear systems using bounded controls , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[16]  Zongli Lin,et al.  Semi-global Exponential Stabilization of Linear Systems Subject to \input Saturation" via Linear Feedbacks , 1993 .

[17]  Héctor Rotstein,et al.  Single-input-single-output H∞-control with time domain constraints , 1993, Autom..

[18]  A. Teel.  Global stabilization and restricted tracking for multiple integrators with bounded controls , 1992 .

[19]  Eduardo Sontag,et al.  Nonlinear output feedback design for linear systems with saturating controls , 1990, 29th IEEE Conference on Decision and Control.

[20]  P. Khargonekar,et al.  State-space solutions to standard H/sub 2/ and H/sub infinity / control problems , 1989 .

[21]  P. Khargonekar,et al.  STATESPACE SOLUTIONS TO STANDARD 2 H AND H? CONTROL PROBLEMS , 1989 .

[22]  Sigurd Skogestad,et al.  Robust control of ill-conditioned plants: high-purity distillation , 1988 .

[23]  M. Gevers,et al.  Fake algebraic Riccati techniques and stability , 1988 .

[24]  I. Petersen.  Disturbance attenuation and H^{∞} optimization: A design method based on the algebraic Riccati equation , 1987 .

[25]  Mathukumalli Vidyasagar,et al.  Optimal rejection of persistent bounded disturbances , 1986 .

[26]  J. Doyle.  Analysis of Feedback Systems with Structured Uncertainty , 1982 .

[27]  G. Zames.  Feedback and optimal sensitivity: Model reference transformations, multiplicative seminorms, and approximate inverses , 1981 .

[28]  V. I. Korobov.  A GENERAL APPROACH TO THE SOLUTION OF THE BOUNDED CONTROL SYNTHESIS PROBLEM IN A CONTROLLABILITY PROBLEM , 1980 .

[29]  A. Fuller.  In-the-large stability of relay and saturating control systems with linear controllers , 1969 .

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