Robust stabilizability of normalized coprime factors: The infinite-dimensional case

The problem of robustly stabilizing a linear system subject to H∞-bounded perturbations in the numerator and the denominator of its normalized left coprime factorization is considered for a class of infinite-dimensional systems. This class has possible unbounded, finite-rank input and output operators, which include many delay and distributed systems. The optimal stability margin is expressed in terms of the solutions of the control and filter algebraic Riccati equations.

[1]  C. Desoer,et al.  An algebra of transfer functions for distributed linear time-invariant systems , 1978 .

[2]  Pramod P. Khargonekar,et al.  On the relation between stable matrix fraction factorizations and regulable realizations of linear systems over rings , 1981, CDC 1981.

[3]  Charles A. Desoer,et al.  Necessary and sufficient condition for robust stability of linear distributed feedback systems , 1982 .

[4]  Dietmar A. Salamon,et al.  On control and observation of neutral systems , 1982 .

[5]  C. Jacobson,et al.  Fractional representation theory: Robustness results with applications to finite dimensional control of a class of linear distributed systems , 1983, The 22nd IEEE Conference on Decision and Control.

[6]  D. Salamon.  Observability of nontrivial small solutions for neutral systems , 1983 .

[7]  Wilhelm Schappacher,et al.  Spectral Properties of Finite-Dimensional Perturbed Linear Semigroups , 1985 .

[8]  Mathukumalli Vidyasagar,et al.  Robust controllers for uncertain linear multivariable systems , 1984, Autom..

[9]  Ruth F. Curtain,et al.  Robust stabilization of infinite dimensional systems by finite dimensional controllers , 1986 .

[10]  D. Salamon.  Infinite Dimensional Linear Systems with Unbounded Control and Observation: A Functional Analytic Approach. , 1987 .

[11]  Franz Kappel,et al.  Spline approximation for retarded systems and the Riccati equation , 1987 .

[12]  A. J. Pritchard,et al.  The linear quadratic control problem for infinite dimensional systems with unbounded input and outpu , 1987 .

[13]  A. Ran,et al.  Optimal Hankel norm model reductions and Wiener-Hopf factorization II: The non-canonical case , 1987 .

[14]  Kazufumi Ito,et al.  Strong convergence and convergence rates of approximating solutions for algebraic riccati equations in Hilbert spaces , 1987 .

[15]  D. Meyer,et al.  A connection between normalized coprime factorizations and linear quadratic regulator theory , 1987 .

[16]  C. Jacobson,et al.  Linear state-space systems in infinite-dimensional space: the role and characterization of joint stabilizability/detectability , 1988 .

[17]  R. Curtain,et al.  Realisation and approximation of linear infinite-dimensional systems with error bounds , 1988 .

[18]  K. Glover,et al.  Robust stabilization of normalized coprime factors: an explicit H∞ solution , 1988, 1988 American Control Conference.

[19]  K. Glover,et al.  Robust stabilization of normalized coprime factor plant descriptions with H/sub infinity /-bounded uncertainty , 1989 .

[20]  Ruth F. Curtain,et al.  Explicit formulas for Hankel norm approximations of infinite-dimensional systems , 1989 .

[21]  George Weiss,et al.  Admissibility of unbounded control operators , 1989 .

[22]  Jonathan R. Partington,et al.  Robust Stabilization of Delay Systems , 1990 .

[23]  T. Georgiou,et al.  Optimal robustness in the gap metric , 1990 .