Mauro Bisiacco

Observer-based Fault Detection and Isolation for 2D State-space Models

In this paper, the fault detection and isolation problems for two-dimensional (2D) state-space models are investigated, both when no disturbances affect the system and when they actually do. Basing on some old results about dead-beat observers [Bisiacco, M. (1986) IEEE Transactions on Automatic Control, AC-31, 676–680] and on some recent results about dead-beat unknown input observers (UIOs) (for 2D systems affected by disturbances) [Bisiacco, M. & Valcher, M. E. (2004) International Journal of Control 77(9), 861–876], we develop a complete theory of dead-beat (possibly unknown input) observer-based fault detectors and isolators (FDIs). Necessary and sufficient conditions for the existence of a dead-beat observer-based FDI or for the existence of a dead-beat UIO-based FDI are derived, and constructive procedures for obtaining such FDIs are described in detail.

On some connections between BIBO and internal stability of two-dimensional filters

Necessary and sufficient conditions are given ensuring that a BIBO stable two-dimensional (2-D) filter admits an internally stable statespace realization. These correspond to the nonexistence of common zeros of the relatively prime numerator and denominator on the unit bidisc distinguished boundary. An equivalent condition is the existence of detectable and stabilizable state space realizations of the transfer function.

The general fault detection and isolation problem for 2D state-space models

Abstract In this paper, the fault detection and isolation problem for two-dimensional (2D) state-space models is investigated in a rather general setting, by assuming that disturbances may affect the system. In a recent contribution [M. Bisiacco, M.E. Valcher, Observer-based fault detection and isolation for 2D state-space models, Multidim. Systems Signal Process 17 (2006) 219–242], a complete theory of dead-beat (possibly unknown input) observer-based fault detectors and isolators (FDIs) has been developed. Here the wider class of 2D FDIs, which allow to detect and identify possible faults, without requiring a preliminary state estimation, is introduced, and necessary and sufficient conditions for the existence of a dead-beat FDI are derived. Constructive procedures for obtaining such FDIs, and comparisons with the results obtained in [M. Bisiacco, M.E. Valcher, Observer-based fault detection and isolation for 2D state-space models, Multidim. Systems Signal Process 17 (2006) 219–242], are also provided.

New results in 2D optimal control theory

The infinite horizon optimal control problem is solved for 2D systems described by the Fornasini-Marchesini model. An ℓ2-approach permits us to reduce the optimal control problem to a norm minimization one in Hilbert spaces. Both necessary and sufficient conditions for solvability and the structure of the solution are established. Moreover, a comparison with known results is presented, and the singularities of the 2D Riccati equation are examined in order to characterize suboptimal control laws that apply whenever the solvability conditions are not satisfied.

Optimal control of two-dimensional systems

Necessary and sufficient conditions for the existence and the uniqueness of the solution of the optimal control problem of discrete-time linear time invariant two-dimensional systems are determined. Given a system that satisfies these conditions, the optimal control law is obtained using an algebraic Riccati equation with coefficients in the polynomial ring

Unknown input observers for 2D state-space models

R[z]

A Behavioral Approach to Estimation and Dead-Beat Observer Design With Applications to State–Space Models

. Since the feedback implementation of this law does not preserve the causal structure of the system, suboptimal control laws are also discussed that lead to a weakly causal two-dimensional system.Finally, some important connections between optimal control in an

A note on the direct sum decomposition of two-dimensional behaviors

\mathfrak{l}_2

Brief Behavior decompositions and two-sided diophantine equations

setting and

Dead-beat estimation problems for 2D behaviors

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