Diagonal stability of stochastic systems subject to nonlinear disturbances and diagonal norms

✍ Scribed by C. Langbort; V. Ugrinovskii

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 381 KB
• Volume: 47
• Category: Article
• ISSN: 0005-1098
• DOI: 10.1016/j.automatica.2011.02.019

✦ Synopsis

A known result in the stability theory of stochastic systems with nonlinear Lipschitz-bounded noise intensity states that the robust stability radius of such a stochastic system is equal to the inverse of the H 2 norm of its 'noise-to-output' transfer function. This paper extends this result to the case where one is interested in the diagonal stability of the system under consideration. This problem arises naturally when studying large-scale interconnected systems subject to random perturbations, as one is often interested in using diagonal or block-diagonal Lyapunov functions for such plants. The main result of the paper is the characterization of the diagonal stochastic stability radius, which is similar to the mentioned result for non-diagonal stability.