A general result on the stabilization of linear systems using bounded controls

We present two constructions of controllers that globally stabilize linear systems subject to control saturation. The only conditions imposed are the obvious necessary ones, namely that no eigenvalues of the uncontrolled system have positive real part and that the standard stabilizability rank condition holds. We use essentially arbitrary saturations /spl sigma/, subject only to the requirement that: (i) /spl sigma/ is locally Lipschitz, (ii) s/spl sigma/(s)>0 whenever s/spl ne/0, (iii) /spl sigma/ is differentiable at 0 and /spl sigma/'(0)>0, and (iv) lim inf/sub |s|/spl rarr//spl infin//|/spl sigma/(s)|>0.<<ETX>>

[1]  Per Hagander,et al.  A new design of constrained controllers for linear systems , 1982, 1982 21st IEEE Conference on Decision and Control.

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

[3]  H. Sussmann,et al.  On the stabilizability of multiple integrators by means of bounded feedback controls , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[4]  Vassilis L. Syrmos,et al.  Computational Observer Design Techniques in Linear Systems with Unknown Inputs using the Concept of Transmission Zeros , 1992, 1992 American Control Conference.

[5]  D. Youla,et al.  Single-loop feedback-stabilization of linear multivariable dynamical plants , 1974, Autom..

[6]  Per-Olof Gutman,et al.  A new design of constrained controllers for linear systems , 1985, IEEE Transactions on Automatic Control.

[7]  Zongli Lin,et al.  Semi-global exponential stabilization of linear systems subject to “input saturation” via linear feedbacks , 1993 .

[8]  N. Krikelis,et al.  Design of tracking systems subject to actuator saturation and integrator wind-up , 1984 .

[9]  Marshall Slemrod.  Feedback stabilization of a linear control system in Hilbert space with ana priori bounded control , 1989, Math. Control. Signals Syst..

[10]  Hughes Helicopters,et al.  On Developing and Flight Testing a Higher Harmonic Control System , 1983 .

[11]  Dennis S. Bernstein,et al.  ON STABLE FULL-ORDER AND REDUCED-ORDER LQG CONTROLLERS , 1991 .

[12]  R. E. Kalman,et al.  Control System Analysis and Design Via the “Second Method” of Lyapunov: I—Continuous-Time Systems , 1960 .

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

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

[15]  C. Ganesh,et al.  Design of Optimal Control Systems with Stable Feedback , 1986, 1986 American Control Conference.

[16]  Eduardo D. Sontag,et al.  Stabilization of Linear Systems with Bounded Controls , 1992 .

[17]  Marimuthu Palaniswami,et al.  Stability of rate constrained robust pole placement adaptive control systems , 1992 .

[18]  J. B. Pearson,et al.  On H2-optimization with stable controllers , 1987, 26th IEEE Conference on Decision and Control.

[19]  Malcolm C. Smith,et al.  On the order of stable compensators , 1986, Autom..

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

[21]  S. Tarbouriech,et al.  Global stability of a class of linear systems with saturated controls , 1992 .

[22]  Eduardo D. Sontag,et al.  Stabilization with Saturated Actuators, a Worked Example: F-8 Longitudinal Flight Control , 1993, Proceedings. The First IEEE Regional Conference on Aerospace Control Systems,.

[23]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[24]  D. Hill,et al.  Dissipative nonlinear systems: basic properties and stability analysis , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[25]  C. Nett,et al.  Minimal Complexity Control Law Synthesis, Part 1: Problem Formulation and Reduction to Optimal Static Output Feedback , 1989, 1989 American Control Conference.

[26]  A. Benzaouia.  The regulator problem for class of linear systems with constrained control , 1988 .

[27]  A. Schaft.  L/sub 2/-gain analysis of nonlinear systems and nonlinear state-feedback H/sub infinity / control , 1992 .

[28]  Robert L. Kosut,et al.  Design of Linear Systems with Saturating Linear Control and Bounded States , 1982, 1982 American Control Conference.

[29]  Dante C. Youla,et al.  Modern Wiener-Hopf Design of Optimal Controllers. Part I , 1976 .

[30]  Eduardo Sontag.  Remarks on stabilization and input-to-state stability , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[31]  Eduardo Sontag.  An algebraic approach to bounded controllability of linear systems , 1984 .

[32]  Eduardo Sontag.  Smooth stabilization implies coprime factorization , 1989, IEEE Transactions on Automatic Control.

[33]  (A, B)-stabilizability conditions with respect to certain Lyapunov functions , 1993, Proceedings of IEEE Systems Man and Cybernetics Conference - SMC.

[34]  Tryphon T. Georgiou,et al.  The parallel projection operators of a nonlinear feedback system , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[35]  Jesus Alvarez,et al.  Linear systems with single saturated input: stability analysis , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[36]  C. Abdallah,et al.  Suboptimal Strong Stabilization Using Fixed-Order Dynamic Compensation , 1990, 1990 American Control Conference.