-admissibility of the right-shift semigroup on

It is shown that the right-shift semigroup on does not satisfy the weighted Weiss conjecture for α(0,1). In other words, α-admissibility of scalar valued observation operators cannot always be characterised by a simple resolvent growth condition. This result is in contrast to the unweighted case, where 0-admissibility can be characterised by a simple growth bound. The result is proved by providing a link between discrete and continuous α-admissibility and then translating a counterexample for the unilateral shift on to continuous time systems.     

Stabilization of some fractional delay systems of neutral type

In this note, we give new stability tests which enable one to fully characterize the H_∞-stability of systems with transfer function , where h>0 and p,q,r are real polynomials in the variable s^μ for 0<μ<1.As an application of this, in the case r(s)=1 and degp=degq=1, families of H_∞-stabilizing controllers are given and a complete parametrization of all H_∞-stabilizing controllers is obtained when .     

Static and output-feedback of discrete-time LTI systems with state multiplicative noise

A parameter dependent approach for designing static output-feedback controller for linear time-invariant systems with state-multiplicative noise is introduced which achieves a minimum bound on either the stochastic H₂ or the H_∞ performance levels. A solution is obtained also for the case where, in addition to the stochastic parameters, the system matrices reside in a given polytope. In this case, a parameter dependent Lyapunov function is described which enables the derivation of the required constant feedback gain via a solution of a set of linear matrix inequalities that correspond to the vertices of the uncertainty polytope.The stochastic parameters appear in both the dynamics and the input matrices of the state space model of the system. The problems are solved using the expected value of the standard performance indices over the stochastic parameters. The theory developed is demonstrated by a simple example.     

control for fast sampling discrete-time singularly perturbed systems

This paper is concerned with the H_∞ control problem via state feedback for fast sampling discrete-time singularly perturbed systems. A new H_∞ controller design method is given in terms of solutions to linear matrix inequalities (LMIs), which eliminates the regularity restrictions attached to the Riccati-based solution. A method for evaluating the upper bound of singular perturbation parameter with meeting a prescribed H_∞ performance bound requirement is also given. Furthermore, the results are extended to robust controller design for fast sampling discrete-time singularly perturbed systems with polytopic uncertainties. Numerical examples are given to illustrate the validity of the proposed methods.     

The complete inclusion structure of leaf power classes

Let k≥2 be an integer and G=(V,E) be a finite simple graph. A tree T is a k-leaf root of G, if V is the set of leaves of T and, for any two distinct x,yV, the distance between x and y in T is at most k if and only if xyE. We say that G is a k-leaf power if there is a k-leaf root of G. The main result of this paper is that, for all 2≤k<k^′, the classes of k- and k^′-leaf powers are inclusion-incomparable, if and only if k^′≤2k−3 and k^′−k is an odd number. With this result, an open problem from the literature about the inclusion structure of these graph classes is solved completely. In addition, the intersection of the smallest pair of inclusion-incomparable classes is studied.     

Improved upper bounds on the L(2,1) -labeling of the skew and converse skew product graphs

An L(2,1)-labeling of a graph G is a function f from the vertex set V(G) to the set of all nonnegative integers such that |f(x)−f(y)|≥2 if d(x,y)=1 and |f(x)−f(y)|≥1 if d(x,y)=2, where d(x,y) denotes the distance between x and y in G. The L(2,1)-labeling number λ(G) of G is the smallest number k such that G has an L(2,1)-labeling with max{f(v):vV(G)}=k. Griggs and Yeh conjecture that λ(G)≤Δ² for any simple graph with maximum degree Δ≥2. This paper considers the graph formed by the skew product and the converse skew product of two graphs with a new approach on the analysis of adjacency matrices of the graphs as in [W.C. Shiu, Z. Shao, K.K. Poon, D. Zhang, A new approach to the L(2,1)-labeling of some products of graphs, IEEE Trans. Circuits Syst. II: Express Briefs (to appear)] and improves the previous upper bounds significantly.     

Minimality considerations for graph energy over a class of graphs

Let G be a graph on n vertices, and let CHP(G;λ) be the characteristic polynomial of its adjacency matrix A(G). All n roots of CHP(G;λ), denoted by , are called to be its eigenvalues. The energy E(G) of a graph G, is the sum of absolute values of all eigenvalues, namely, . Let be the set of n-vertex unicyclic graphs, the graphs with n vertices and n edges. A fully loaded unicyclic graph is a unicyclic graph taken from with the property that there exists no vertex with degree less than 3 in its unique cycle. Let be the set of fully loaded unicyclic graphs. In this article, the graphs in with minimal and second-minimal energies are uniquely determined, respectively.     

Robust control of uncertain differential linear repetitive processes

For two-dimensional (2-D) systems, information propagates in two independent directions. 2-D systems are known to have both system-theoretical and applications interest, and the so-called linear repetitive processes (LRPs) are a distinct class of 2-D discrete linear systems. This paper is concerned with the problem of L₂–L_∞ (energy to peak) control for uncertain differential LRPs, where the parameter uncertainties are assumed to be norm-bounded. For an unstable LRP, our attention is focused on the design of an L₂–L_∞ static state feedback controller and an L₂–L_∞ dynamic output feedback controller, both of which guarantee the corresponding closed-loop LRPs to be stable along the pass and have a prescribed L₂–L_∞ performance. Sufficient conditions for the existence of such L₂–L_∞ controllers are proposed in terms of linear matrix inequalities (LMIs). The desired L₂–L_∞ dynamic output feedback controller can be found by solving a convex optimization problem. A numerical example is provided to demonstrate the effectiveness of the proposed controller design procedures.     

Input–output approach to stability and -gain analysis of systems with time-varying delays

Stability and L₂ (l₂)-gain of linear (continuous-time and discrete-time) systems with uncertain bounded time-varying delays are analyzed under the assumption that the nominal delay values are not equal to zero. The delay derivatives (in the continuous-time) are not assumed to be less than q<1. An input–output approach is applied by introducing a new input–output model, which leads to effective frequency domain and time domain criteria. The new method significantly improves the existing results for delays with derivatives not greater than 1, which were treated in the past as fast-varying delays (without any constraints on the delay derivatives). New bounded real lemmas (BRLs) are derived for systems with state and objective vector delays and norm-bounded uncertainties. Numerical examples illustrate the efficiency of the new method.     

Observers for a class of Lipschitz systems with extension to performance analysis

In this paper, observer design for a class of Lipschitz nonlinear dynamical systems is investigated. One of the main contributions lies in the use of the differential mean value theorem (DMVT) which allows transforming the nonlinear error dynamics into a linear parameter varying (LPV) system. This has the advantage of introducing a general Lipschitz-like condition on the Jacobian matrix for differentiable systems. To ensure asymptotic convergence, in both continuous and discrete time systems, such sufficient conditions expressed in terms of linear matrix inequalities (LMIs) are established. An extension to H_∞ filtering design is obtained also for systems with nonlinear outputs. A comparison with respect to the observer method of Gauthier et al. [A simple observer for nonlinear systems. Applications to bioreactors, IEEE Trans. Automat. Control 37(6) (1992) 875–880] is presented to show that the proposed approach avoids high gain for a class of triangular globally Lipschitz systems. In the last section, academic examples are given to show the performances and some limits of the proposed approach. The last example is introduced with the goal to illustrate good performances on robustness to measurement errors by avoiding high gain.     

Suboptimal robust synthesis for MIMO plant under coprime factor perturbations

Suboptimal robust synthesis for MIMO nominal system under coprime factor perturbations is considered in classical and non-classical statements. In the classical statement, weights of perturbations and upper bound on magnitude bounded exogenous disturbance are assumed to be known to controller designer. Suboptimal synthesis within ε tolerance is reduced to the solution of log₂(1/ε) standard mixed sensitivity problems of ℓ₁ optimization. In the non-classical statement, the upper bounds on perturbations and exogenous disturbance are to be estimated from measurement data and suboptimal synthesis is reduced to the solution of 1/ε mixed sensitivity problems.     

Reduced-order filtering for singular systems

This paper solves the problem of reduced-order H_∞ filtering for singular systems. The purpose is to design linear filters with a specified order lower than the given system such that the filtering error dynamic system is regular, impulse-free (or causal), stable, and satisfies a prescribed H_∞ performance level. One major contribution of the present work is that necessary and sufficient conditions for the solvability of this problem are obtained for both continuous and discrete singular systems. These conditions are characterized in terms of linear matrix inequalities (LMIs) and a coupling non-convex rank constraint. Moreover, an explicit parametrization of all desired reduced-order filters is presented when these inequalities are feasible. In particular, when a static or zeroth-order H_∞ filter is desired, it is shown that the H_∞ filtering problem reduces to a convex LMI problem. All these results are expressed in terms of the original system matrices without decomposition, which makes the design procedure simple and directly. Last but not least, the results have generalized previous works on H_∞ filtering for state-space systems. An illustrative example is given to demonstrate the effectiveness of the proposed approach.     

Dual periodicity in -norm minimisation problems

The topic of this paper is the discrete-time l₁-norm minimisation problem with convolution constraints. We find primal initial conditions for which the dual optimal solution is periodic. Periodicity of the dual optimal solution implies satisfaction of a simple linear recurrence relation by the primal optimal solution.     

estimation for discrete-time piecewise homogeneous Markov jump linear systems

This paper concerns the problem of H_∞ estimation for a class of Markov jump linear systems (MJLS) with time-varying transition probabilities (TPs) in discrete-time domain. The time-varying character of TPs is considered to be finite piecewise homogeneous and the variations in the finite set are considered to be of two types: arbitrary variation and stochastic variation, respectively. The latter means that the variation is subject to a higher-level transition probability matrix. The mode-dependent and variation-dependent H_∞ filter is designed such that the resulting closed-loop systems are stochastically stable and have a guaranteed H_∞ filtering error performance index. Using the idea in the recent studies of partially unknown TPs for the traditional MJLS with homogeneous TPs, a generalized framework covering the two kinds of variations is proposed. A numerical example is presented to illustrate the effectiveness and potential of the developed theoretical results.     

On admissible pairs and equivalent feedback—Youla parameterization in iterative learning control

This paper revisits a well-known synthesis problem in iterative learning control, where the objective is to optimize a performance criterion over a class of causal iterations. The approach taken here adopts an infinite-time setting and looks at limit behavior.The first part of the paper considers iterations without current-cycle-feedback (CCF) term. A notion of admissibility is introduced to distinguish between pairs of operators that define a robustly converging iteration and pairs that do not. The set of admissible pairs is partitioned into disjoint equivalence classes. Different members of an equivalence class are shown to correspond to different realizations of a (stabilizing) feedback controller. Conversely, every stabilizing controller is shown to allow for a (non-unique) factorization in terms of admissible pairs. Class representatives are introduced to remove redundancy. The smaller set of representative pairs is shown to have a trivial parameterization that coincides with the Youla parameterization of all stabilizing controllers (stable plant case).The second part of the paper considers the general family of CCF-iterations. Results derived in the non-CCF case carry over, with the exception that the set of equivalent controllers now forms but a subset of all stabilizing controllers. Necessary and sufficient conditions for full generalization are given.     

Isolation concepts for efficiently enumerating dense subgraphs

In an undirected graph G=(V,E), a set of k vertices is called c-isolated if it has less than ck outgoing edges. Ito and Iwama [H. Ito, K. Iwama, Enumeration of isolated cliques and pseudo-cliques, ACM Transactions on Algorithms (2008) (in press)] gave an algorithm to enumerate all c-isolated maximal cliques in O(4^cc⁴|E|) time. We extend this to enumerating all maximal c-isolated cliques (which are a superset) and improve the running time bound to O(2.89^cc²|E|), using modifications which also facilitate parallelizing the enumeration. Moreover, we introduce a more restricted and a more general isolation concept and show that both lead to faster enumeration algorithms. Finally, we extend our considerations to s-plexes (a relaxation of the clique notion), providing a W[1]-hardness result when the size of the s-plex is the parameter and a fixed-parameter algorithm for enumerating isolated s-plexes when the parameter describes the degree of isolation.     

VCPSS: A two-in-one two-decoding-options image sharing method combining visual cryptography (VC) and polynomial-style sharing (PSS) approaches

This paper presents a novel method to combine two major branches of image sharing: VC and PSS. n transparencies are created for a given gray-valued secret image. If the decoding computer is temporarily not available at (or, not connected to) the decoding scene, we can still physically stack any t received transparencies (tn is a threshold value) to get a vague black-and-white view of the secret image immediately. On the other hand, when the decoding computer is finally available, then we can get a much finer gray-valued view of the secret image using the information hidden in the transparencies. In summary, each transparency is a two-in-one carrier of the information, and the decoding has two options.     

filtering for uncertain stochastic time-delay systems with sector-bounded nonlinearities

In this paper, we deal with the robust H_∞ filtering problem for a class of uncertain nonlinear time-delay stochastic systems. The system under consideration contains parameter uncertainties, Itô-type stochastic disturbances, time-varying delays, as well as sector-bounded nonlinearities. We aim at designing a full-order filter such that, for all admissible uncertainties, nonlinearities and time delays, the dynamics of the filtering error is guaranteed to be robustly asymptotically stable in the mean square, while achieving the prescribed H_∞ disturbance rejection attenuation level. By using the Lyapunov stability theory and Itô’s differential rule, sufficient conditions are first established to ensure the existence of the desired filters, which are expressed in the form of a linear matrix inequality (LMI). Then, the explicit expression of the desired filter gains is also characterized. Finally, a numerical example is exploited to show the usefulness of the results derived.