Linear state-space systems in infinite-dimensional space: the role and characterization of joint stabilizability/detectability

Several fundamental results from the theory of linear state-space systems in finite-dimensional space are extended to encompass a class of linear state-space systems in infinite-dimensional space. The results treated are those pertaining to the relationship between input-output and internal stability, the problem of dynamic output feedback stabilization, and the concept of joint stabilizability/detectability. A complete structural characterization of jointly stabilizable/detectable systems is obtained. The generalized theory applies to a large class of linear state-space systems, assuming only that: (i) the evolution of the state is governed by a strongly continuous semigroup of bounded linear operators; (ii) the state space is Hilbert space; (iii) the input and output spaces are finite-dimensional; and (iv) the sensing and control operators are bounded. General conclusions regarding the fundamental structure of control-theoretic problems in infinite-dimensional space can be drawn from these results. >

[1]  R. Triggiani.  On the stabilizability problem in Banach space , 1975 .

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

[3]  A. J. Pritchard,et al.  Stability and Stabilizability of Infinite-Dimensional Systems , 1981 .

[4]  Mark J. Balas,et al.  Trends in large space structure control theory: Fondest hopes, wildest dreams , 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]  Amit Bhaya,et al.  Absolute k-stability of linear distributed n-ports , 1985 .

[7]  E. Kamen,et al.  Stabilization of time-delay systems using finite-dimensional compensators , 1985, IEEE Transactions on Automatic Control.

[8]  C. Nett.  Algebraic aspects of linear control system stability , 1985, 1985 24th IEEE Conference on Decision and Control.

[9]  Kameshwar Poolla,et al.  Robust stabilization of distributed systems , 1986, Autom..

[10]  A. Tannenbaum,et al.  Gain optimization for distributed plants , 1986 .

[11]  Joseph J. Winkin,et al.  DISTRIBUTED SYSTEM TRANSFER FUNCTIONS OF EXPONENTIAL ORDER. , 1986 .

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

[13]  Hartmut Logemann.  On the existence of finite-dimensional compensators for retarded and neutral systems , 1986 .

[14]  J. Doyle,et al.  Linear control theory with an H ∞ 0E optimality criterion , 1987 .