Filtering for uncertain 2-D discrete systems with state delays

Abstract

This paper is concerned with the problem of robust H ∞ filtering for two-dimensional (2-D) discrete systems with time delays in states. The 2-D systems under consideration are described in terms of the well-known Fornasini-Marchesini local state-space (FMLSS) models with time-delays. Our attention is focused on the design of a full-order filter such that the filtering error system is guaranteed to be asymptotically stable with a prescribed H ∞ disturbance attenuation performance. Sufficient conditions for the existence of desired filters are established by using a linear matrix inequality (LMI) approach, and the corresponding filter design problem is then cast into a convex optimization problem that can be efficiently solved by resorting to some standard numerical software. Furthermore, the obtained results are extended to more general cases where the system matrices contain either polytopic or norm-bounded parameter uncertainties. A simulation example is provided to illustrate the effectiveness of the proposed design method.

H ∞ filtering for Markovian jump delay systems with parameter uncertainties and limited communication capacity

“…The results in [14] show that the effect of non-minimum phase zeros and plant relative degree vanishes when channel feedback is available. These conclusions are consistent with previous results derived for signal-to-noise (SNR) constrained channels in [16]. The effect of channel pre-and post-processing is also analysed in [14] yielding conclusions that are similar to those obtained for SNR constrained channels in [17].…”

“…A relevant feature of such architecture is that, if available, the controller can exploit delayed channel feedback (or, equivalently, delayed controller to actuator channel state information). Channel feedback is known to allow one to reduce the minimal SNR required for stabilisation over an additive white noise channel, when compared to standard one degree-of-freedom architectures [16]. As already foreshadowed before, similar conclusion can be drawn when communication takes place over a fading channel [14].…”

Output Feedback H ∞ Control for 2-D State-Delayed Systems

“…Noting this, using equation (13) and then following a similar line as in the proof of Theorem 3 in [20], we have that system (1) with ω(i, j ) = 0 is asymptotically stable if LMIs (5) and (6) are feasible.…”

“…Most results for the 2-D problems focused on systems without delays, though for specific stability, control and filtering problems of 2-D state-delayed systems were considered in [14][15][16] and [2,20], respectively. It is only for convenience and for the avoidance of analytical, structural and computational complexities that there are no delay-independent or delay-dependent H ∞ output feedback control results for 2-D systems.…”

Analysis and Design of $$H_{\infty }$$ H ∞ Controllers for 2D Singular Systems with Delays

“…Of these previous results, the H ∞ filtering problem for 2D linear systems has been studied in [2,7,8,[10][11][12]15,27,28,[30][31][32][33][34]41]; for 2D linear parameter-varying systems, the related work can be found in [9,32]; for 2D systems with delays, this filtering problem has been investigated in [27,31]; the stability and stabilization of 2D systems have been solved in [1,[17][18][19]26], while the H ∞ control for 2D nonlinear systems with delays and the nonfragile H ∞ and l 2 − l 1 problems were studied in [36]. Nonetheless, as no systematic and general approach to analyze 2D SRM systems exists, there are still many unsolved problems.…”