Fornasini-Marchesini Second Local State-space Research Articles

Novel Realizability Criterion for Saturation Overflow Oscillation-Free 2-D Digital Filters Based on the Fornasini-Marchesini Second Model

The problem of global asymptotic stability (GAS) of two-dimensional (2-D) digital filters based on the Fornasini-Marchesini second local state-space (FMSLSS) model with saturation arithmetic is studied in this paper. A novel GAS criterion for the 2-D digital filter is presented. The obtained criterion is compared with several previously reported criteria.

Stability of Uncertain 2-D Discrete Systems in Presence of Generalized Overflow Nonlinearities

Stability analysis of two-dimensional (2-D) discontinuous systems with generalized overflow nonlinear effects is considered in this work. The 2-D models considered are the well-known Fornasini Marchesini Second Local State-Space (FMSLSS) model and the Roesser model. The effect of uncertainties and interim-like variable time-delays on the system is also examined in the study. Using reciprocally convex approach we provide stability criteria which is organized as matrix inequalities. Numerical illustrations are given to demonstrate the applicability of the results.

Stability criterion for uncertain 2-$D$ discrete systems with interval-like time-varying delay employing quantization/overflow nonlinearities

This paper considers the problem of global asymptotic stability of a class of two-dimensional (2-$D$) uncertain discrete systems described by the Fornasini-Marchesini second local state-space (FMSLSS) model under the influence of various combinations of quantization/overflow nonlinearities and interval-like time-varying delay in the state. The systems under consideration involve parameter uncertainties that are assumed to be deterministic and norm-bounded. A delay-dependent stability criterion is established by bounding the forward difference of the 2-$D$ Lyapunov functional using the reciprocally convex approach. The criterion is compared with a recently reported criterion.

A note on stability analysis of 2-D linear discrete systems based on the Fornasini–Marchesini second model: Stability with asymmetric Lyapunov matrix

A recently reported Lyapunov based criterion (Singh (2014) [7]) for the asymptotic stability of two-dimensional (2-D) linear discrete systems described by the Fornasini–Marchesini second local state-space (FMSLSS) model is reviewed. It is established in this paper that, despite utilizing a more general Lyapunov matrix, Singh's criterion will never lead to an enhanced stability region in the parameter-space as compared to that obtainable via Hinamoto–Lu's criterion.

An LMI based criterion for the global asymptotic stability of 2-D discrete state-delayed systems with saturation nonlinearities

This paper deals with the problem of global asymptotic stability of a class of two-dimensional (2-D) discrete systems described by the Fornasini–Marchesini second local state-space (FMSLSS) model in presence of saturation nonlinearities and state delays in each of the two independent directions of information propagation. A linear matrix inequality (LMI) based criterion for the global asymptotic stability of such systems is presented. It is shown that several previously reported stability criteria for 2-D discrete FMSLSS model with saturation nonlinearities are recovered from the presented approach as special cases.

Stability Analysis of 2D Discrete Linear System Described by the Fornasini-Marchesini Second Model with Actuator Saturation

This paper proposes a novel antiwindup controller for 2D discrete linear systems with saturating controls in Fornasini-Marchesini second local state space (FMSLSS) setting. A Lyapunov-based method to design an antiwindup gain of 2D discrete systems with saturating controls is established. Stability conditions allowing the design of antiwindup loops, in both local and global contexts have been derived. Numerical examples are provided to illustrate the applicability of the proposed method.

Robust Non-Fragile Control of 2-D Discrete Uncertain Systems: An LMI Approach

This paper considers the problem of robust non-fragile control for a class of two-dimensional (2-D) discrete uncertain systems described by the Fornasini-Marchesini second local state-space (FMSLSS) model under controller gain variations. The parameter uncertainty is assumed to be norm-bounded. The problem to be addressed is the design of non-fragile robust controllers via state feedback such that the resulting closed-loop system is asymptotically stable for all admissible parameter uncertainties and controller gain variations. A sufficient condition for the existence of such controllers is derived based on the linear matrix inequality (LMI) approach combined with the Lyapunov method. Finally, a numerical example is illustrated to show the contribution of the main result.

LMI Approach to Suboptimal Guaranteed Cost Control for 2-D Discrete Uncertain Systems

This paper studies the problem of the guaranteed cost control via static-state feedback controllers for a class of two-dimensional (2-D) discrete systems described by the Fornasini-Marchesini second local state-space (FMSLSS) model with norm bounded uncertainties. A convex optimization problem with linear matrix inequality (LMI) constraints is formulated to design the suboptimal guaranteed cost controller which ensures the quadratic stability of the closed-loop system and minimizes the associated closed-loop cost function. Application of the proposed controller design method is illustrated with the help of one example.

LMI-Based Criterion for the Robust Stability of 2D Discrete State-Delayed Systems Using Generalized Overflow Nonlinearities

This paper addresses the problem of global asymptotic stability of a class of discrete uncertain state-delayed systems described by the Fornasini-Marchesini second local state-space (FMSLSS) model using generalized overflow nonlinearities. The uncertainties are assumed to be norm bounded. A computationally tractable, that is, linear-matrix-inequality-(LMI-) based new criterion for the global asymptotic stability of such system is proposed. It is demonstrated that several previously reported stability criteria for two-dimensional (2D) systems are recovered from the presented approach as special cases. Numerical examples are given to illustrate the usefulness of the presented approach.

An improved LMI-based criterion for the design of optimal guaranteed cost controller for 2-D discrete uncertain systems

An improved criterion for the design of optimal static-state feedback guaranteed cost controller for two-dimensional (2-D) discrete uncertain systems described by the Fornasini–Marchesini second local state-space (FMSLSS) model is proposed. The design problem of the optimal guaranteed cost controller is formulated as a convex optimization problem with linear matrix inequality (LMI) constraints. The proposed method yields tighter upper bound of the closed-loop cost function as compared to a recently reported method.

Robust stability of 2-D discrete systems employing generalized overflow nonlinearities: An LMI approach

This paper deals with the problem of global asymptotic stability of a class of uncertain discrete systems described by the Fornasini–Marchesini second local state-space (FMSLSS) model using generalized overflow nonlinearities. The systems under investigation involve parameter uncertainties that are assumed to be deterministic and norm bounded. An LMI-based criterion for the global asymptotic stability of such systems is proposed. The proposed criterion is compared with previously reported criteria.

Optimal guaranteed cost control of 2 -D discrete uncertain systems: An LMI approach

This paper addresses the problem of the optimal guaranteed cost control for a class of two-dimensional (2-D) discrete systems described by the Fornasini–Marchesini second local state-space (FMSLSS) model with norm-bounded uncertainties. A linear matrix inequality (LMI)-based new criterion for the existence of a state feedback controller which guarantees not only the asymptotic stability of the closed-loop system, but also an adequate performance bound over all the possible parameter uncertainties is established. Furthermore, a convex optimization problem with LMI constraints is formulated to design the optimal guaranteed cost controller which minimizes the upper bound of the closed-loop cost function.

LMI-based criterion for the robust guaranteed cost control of 2 -D systems described by the Fornasini–Marchesini second model

This paper considers the problem of the guaranteed cost control for a class of two-dimensional (2-D) discrete systems described by the Fornasini–Marchesini second local state–space (FMSLSS) model with norm-bounded uncertainties. An improved linear matrix inequality (LMI)-based criterion for the existence of robust guaranteed cost controller is established. Such controllers render the closed-loop system asymptotically stable for all admissible uncertainties and guarantee an adequate level of performance.