| Full text | |
| Author(s): |
Ribeiro, Junior R.
;
Romero, Luiz H.
;
Costa, Eduardo F.
;
Todorov, Marcos G.
Total Authors: 4
|
| Document type: | Journal article |
| Source: | IEEE CONTROL SYSTEMS LETTERS; v. 7, p. 6-pg., 2023-01-01. |
| Abstract | |
In this note, we consider a general class of stochastic, jump parameter systems and show that the so-called H-2 norm is the Frobenius norm of the impulse response matrix of the system. We present a necessary and sufficient condition for the H-2 norm to be the induced norm from the input to the output for a particular type of deterministic input signal. As expected in the context of time-varying systems, we cannot extend this result to more general deterministic input signals. Moreover, finite H-2 norm does not prevent infinite norm output in response to a finite norm input, unless additional conditions are imposed on the system. Here, we give relatively mild conditions - mean square stability and jumps driven by a finite-dimensional Markov chain starting in equilibrium - and we show that finite H-2 norm implies a bounded ratio between the norms of the output and the input, for certain suitable norms. (AU) | |
| FAPESP's process: | 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry |
| Grantee: | Francisco Louzada Neto |
| Support Opportunities: | Research Grants - Research, Innovation and Dissemination Centers - RIDC |