Stabilization of two-dimensional nonlinear systems described by Fornasini-Marchesini and Roesser models

Pakshin, Pavel, Emelianova, Julia, Gałkowski, Krzysztof and Rogers, Eric (2018) Stabilization of two-dimensional nonlinear systems described by Fornasini-Marchesini and Roesser models. SIAM Journal on Control and Optimization, 56 (5), 3848-3866. (doi:10.1137/16M1076575).

Abstract

The paper considers nonlinear two-dimensional systems described by the Fornasini-Marchesini or Roesser state-space models. Conditions for such systems to have a physically motivated exponential stability property are derived using vector Lyapunov functions. A form of passivity, termed exponential passivity, is introduced and used, together with a vector storage function, to develop a feedback based control law that guarantees exponential stability of the controlled system. For cases where noise is present, stochastic dissipativity in the second moment is defined and then a particular case of this property, termed passivity in the mean square, is used, together with a vector storage function, to develop a feedback based control law such that the controlled system also has this property. Two physically motivated particular cases, a system with nonlinear actuator dynamics and additive noise and a linear system with state-dependent noise, respectively, are also considered to demonstrate the effectiveness of the new results.

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Contributors

Author: Eric Rogers

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