Haranath Kar

Stability of 2-D systems described by the Fornasini-Marchesini first model

A sufficient condition for the stability of linear two-dimensional (2-D) systems described by the Fornasini-Marchesini (1976) first model is presented. The condition is compared with previously reported conditions.

Stability analysis of 1-D and 2-D fixed-point state-space digital filters using any combination of overflow and quantization nonlinearities

A new criterion, together with its frequency-domain interpretation for the global asymptotic stability of zero-input one-dimensional (1-D) state-space digital filters under various combinations of overflow and quantization nonlinearities and for the situation where quantization occurs after summation only, is presented. A condition in closed form involving solely the parameters of the state transition matrix for the nonexistence of limit cycles in second-order digital filters is derived. Improved versions of some of the stability results due to Leclerc and Bauer (1994) are established. Finally, the approach is extended to two-dimensional (2-D) digital filters described by the Roesser and the Fornasini-Marchesini second local state-space models.

Robust stability of 2-D discrete systems described by the Fornasini-Marchesini second model employing quantization/overflow nonlinearities

New criteria for the global asymptotic stability of the uncertain two-dimensional (2-D) discrete systems described by the Fornasini-Marchesini second local state-space model under various combinations of overflow and quantization nonlinearities are established. Sufficient conditions for the uncertain 2-D discrete systems to be free of overflow oscillations under a generalized overflow arithmetic are presented.

A new criterion for the overflow stability of second-order state-space digital filters using saturation arithmetic

Two recent approaches (one due to Singh [1990] and the other due to Liu and Michel [1992]) for the elimination of zero-input overflow oscillations in state-space digital filters designed with saturation arithmetic are compared. It is demonstrated that Singhs approach leads to a relatively less stringent condition for the nonexistence of overflow oscillations. Using Singhs approach, an improved version of Ritzerfeld-Werters criterion for the nonexistence of overflow oscillations in second-order state-space digital filters is made available. Finally, a new zero-input limit cycle-free realizability condition for a generalized overflow characteristic is presented.

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.

Improved Routh-Pade/spl acute/ approximants: a computer-aided approach

A geometric programming based computer-aided method to derive a reduced order (rth-order) approximant for a given (stable) SISO linear continuous-time system is presented. In this method, stability and the first r time moments/Markov parameters are preserved as well as the errors between a set of subsequent time moments/Markov parameters of the system and those of the model are minimized.

Robust stability of discrete-time state-delayed systems with saturation nonlinearities: Linear matrix inequality approach

This paper addresses the problem of global asymptotic stability of a class of uncertain discrete-time state-delayed systems employing saturation nonlinearities. The parameter uncertainties are assumed to be norm-bounded. A linear matrix inequality (LMI)-based new criterion for the global asymptotic stability of such systems is presented. It is shown that several previously reported stability criteria for systems with saturation nonlinearities are recovered from the presented approach as special cases.

A new sufficient condition for the global asymptotic stability of 2-D state-space digital filters with saturation arithmetic

A new sufficient condition for the global asymptotic stability of two-dimensional (2-D) state-space digital filters described by the Roesser model employing saturation arithmetic is presented. The new condition not only unifies a string of previous stability results, but also yields improvement over them, hence enlarging the overflow stability region of 2-D digital filters.

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.

Stability analysis of 2-D digital filters described by the Fornasini-Marchesini second model using overflow nonlinearities

This paper discusses new criteria for the global asymptotic stability of two-dimensional (2-D) digital filters described by the Fernasini-Marchesini second local state-space model subject to overflow nonlinearities. For saturation and triangular arithmetics, the presented approach will always lead to a larger overflow stability region in the parameter-space, as compared to a recent criterion due to Liu; for other overflow nonlinearities, new criteria may generally provide results as supplement to those obtainable from Lius criterion. The approach leads to a more relaxed saturation overflow stability condition, as compared to a recent criterion due to Hinamoto. Finally, the approach is extended to the situations involving quantization nonlinearities.