Lyapunov functions for time-relevant systems, with application to first-orthant stable systems

Self Cite

We identify a general, i.e. not necessarily denominator-separable Roesser model from 2D discrete vector-geometric trajectories generated by a controllable, quarter-plane causal system. Our procedure consists of two steps: the first one is the computation of state trajectories from the factorization of constant matrices directly constructed from input-output data. The second step is the computation of the state, output, and input matrices of a Roesser model as solutions of a system of linear equations involving the given input-output data and the computed state trajectories.

Section: D Bilinear-and Quadratic Difference Formsmentioning

confidence: 99%

Discrete Roesser state models from 2D frequency data

Rapisarda

2018

Self Cite

“…Interestingly, the existing notion of characteristic sets of discrete 2D systems appears to have taken shape following (Valcher 2000): the characteristic sets of discrete 2D systems dealt with in the literature are predominantly either convex cones or half-spaces (see Rapisarda and Rocha 2012; for some recent examples that incorporate similar notions of characteristic sets). Perhaps the important significance of such characteristic sets lies in their applications in conic stability analysis.…”

Section: Introductionmentioning

confidence: 99%

Every discrete 2D autonomous system admits a finite union of parallel lines as a characteristic set

Pal

2015

In this paper, we show that every discrete 2D autonomous system, that is described by a set of linear partial difference equations with constant real coefficients, admits a finite union of parallel lines as a characteristic set. In order to prove our claim, we first look at a special class of scalar discrete 2D systems and provide such characteristic sets for systems in this class. This special class has the property that systems in this class have their quotient rings to be finitely generated modules over a one-variable Laurent polynomial subring of the original two-variable Laurent polynomial ring in the shift operators. We show that such systems always admit a finite collection of horizontal lines for a characteristic set. We then extend this result to non-scalar discrete 2D autonomous systems. We achieve this in two steps: first, we show that every scalar discrete 2D system can be converted into a system in the above-mentioned class by a coordinate transformation on the independent variables set, Z 2 . Using this we then show that characteristic sets for the original system can be found by applying the inverse coordinate transformation on characteristic sets of the transformed system. Since the transformed system, by virtue of being in the special class, admits a finite union of horizontal lines as a characteristic set, the original system is guaranteed to admit a characteristic set that is a coordinate transformation applied to a finite union of horizontal lines. The coordinate transformation maps this union of horizontal lines to a union of parallel, but possibly tilted, lines. In the next step, we generalize the scalar case to the general vector case: that is, systems with more than one dependent variables. The main motivation for studying characteristic sets that are unions of finitely many parallel lines is that, arguably, such sets can be called "thin" in Z 2 in comparison to the prevalent notions of convex cones and half-spaces as characteristic sets (see "Appendix 1").

“…From (17), and using the fact that the columns of V c form an orthonormal basis for V, it follows that V c G = V c ΩU . The claim follows.…”

Section: Construction Of Internally and Externally Stabilizing Gains mentioning

confidence: 99%

“…Another aspect to consider is that the approach used in this paper still treats all independent variables to be on an equal footing, while for most applications one of the independent variable is time. A "time-relevant" fault estimation framework is needed, where the distinguished role of the independent variable time in the modeling of the fault and in its estimation is recognized and exploited to provide better performance (on time-relevant systems, see also [13,17]). …”

Section: Conclusion and Further Workmentioning

confidence: 99%

Failure identification for 3D linear systems

Maleki

Rapisarda

Ntogramatzidis

et al. 2013

Geometric control theory is used to investigate the problem of fault detection and isolation for 3D linear systems described by FornasiniMarchesini models with the aim using these results in applications areas such as wireless sensor networks.. Necessary and sufficient conditions for the existence of a solution to this problem are established together with constructive methods for the design of observers for fault detection and identification.