Name
Title | ||
|---|---|---|
Optimal Input-Output Stabilization of Infinite-Dimensional Discrete Time-Invariant Linear Systems by Output Injection |
Abstract | ||
|---|---|---|
We study the optimal input-output stabilization of discrete time-invariant linear systems in Hilbert spaces by output injection. We show that a necessary and sufficient condition for this problem to be solvable is that the transfer function has a left factorization over H-infinity. Another equivalent condition is that the filter Riccati equation (of an arbitrary realization) has a solution (in general, unbounded and even nondensely defined). We further show that after renorming the state space in terms of the inverse of the smallest solution of the filter Riccati equation, the closed-loop system is not only input-output stable but also strongly internally $*$-stable. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1137/090762233 | SIAM J. Control and Optimization |
Keywords | Field | DocType |
discrete time-invariant linear system,arbitrary realization,sufficient condition,optimal input-output stabilization,smallest solution,equivalent condition,hilbert space,infinite-dimensional discrete time-invariant linear,filter riccati equation,left factorization,output injection,closed-loop system,riccati equation,discrete time,linear system,input output | Hilbert space,Mathematical optimization,Linear system,Mathematical analysis,Transfer function,Algebraic Riccati equation,Invariant (mathematics),Riccati equation,Discrete time and continuous time,State space,Mathematics | Journal |
Volume | Issue | ISSN |
48 | 8 | 0363-0129 |
Citations | PageRank | References |
1 | 0.38 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Mark R. Opmeer | 1 | 87 | 15.71 |
| Olof J. Staffans | 2 | 66 | 15.08 |