A spectral test for observability and reachability of time-varying systems

SIAM Journal on Control and Optimization

Volumn 37, Issue 5, 1999, Pages 1330-1345

  Peters, M A ^a   Iglesias, P A ^a  

^a Johns Hopkins University   (United States)

Author keywords

Controllability; Discrete time systems; Exponential stability; Observability; Operator theoretic methods; Time varying systems

Indexed keywords

CONTROLLABILITY; DISCRETE TIME CONTROL SYSTEMS; EIGENVALUES AND EIGENFUNCTIONS; LINEAR CONTROL SYSTEMS; MATHEMATICAL OPERATORS; MATRIX ALGEBRA; OBSERVABILITY; SET THEORY; SPECTRUM ANALYSIS; STATE SPACE METHODS; SYSTEM STABILITY;

EXPONENTIAL STABILITY; OPERATOR THEORETIC METHODS; POPOV-BELEVITCH-HAUTUS TEST; SPECTRAL TEST;

TIME VARYING CONTROL SYSTEMS;

EID: 0033140574     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012997321826     Document Type: Article

References (10)

1. B. ANDERSON AND J. MOORE, Detectability and stabilizability of time-varying discrete-time linear systems, SIAM J. Control Optim., 19 (1981), pp. 20-32.
2. B. BEAUZAMY, Introduction to Operator Theory and Invariant Subspaces, North-Holland, Amsterdam, The Netherlands, 1988.
3. W. HAGER AND L. HOROTWITZ, Convergence and stability properties of the discrete riccati operator equation and the associated optimal control and filtering problems, SIAM J. Control Optim., 14 (1976), pp. 295-312.
4. A. HALANAY AND V. IONESCU, Time-Varying Discrete Linear Systems, Oper. Theory Adv. Appl. 68, Birkhäuser, Basel, Switzerland, 1994.
5. E. KAMEN, P. KHARGONEKAR, AND K. POOLLA, A transfer-function approach to linear timevarying discrete-time systems, SIAM J. Control Optim., 23 (1985), pp. 550-565.
6. [C] J. MOORE AND B. ANDERSON, Coping with singular transition matrices in estimation and control stability theory, Internat. J. Control, 31 (1980), pp. 571-586.
7. M. PETERS AND P. IGLESIAS, Minimum Entropy Control for Time-Varying Systems, Birkhäuser, Boston, MA, 1997.
8. K. PRZYLUSKI AND S. ROLEWICZ, On the stability of linear time-varying infinite-dimensional discrete-time systems, Systems Control Lett., 4 (1984), pp. 307-315.
9. W. RUGH, Linear System Theory, 2nd ed., Prentice-Hall, Englewood Cliffs, NJ, 1996.
10. A. SHIELDS, Weighted shift operators and analytic function theory, in Topics in Operator Theory, C. Pearcy, ed., Math. Surveys Monogr. 13, American Mathematical Society, Providence, RI, 1974, pp. 49-128.