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 .     

Strong convergence theorems for a new iterative method of -strictly pseudo-contractive mappings in Hilbert spaces

In this paper, we introduce a new iterative method of a k-strictly pseudo-contractive mapping for some 0≤k<1 and prove that the sequence {x_n} converges strongly to a fixed point of T, which solves a variational inequality related to the linear operator A. Our results have extended and improved the corresponding results of Y.J. Cho, S.M. Kang and X. Qin [Some results on k-strictly pseudo-contractive mappings in Hilbert spaces, Nonlinear Anal. 70 (2008) 1956–1964], and many others.     

Probabilistic π-Calculus and Event Structures

This paper proposes two semantics of a probabilistic variant of the π-calculus: an interleaving semantics in terms of Segala automata and a true concurrent semantics, in terms of probabilistic event structures. The key technical point is a use of types to identify a good class of non-deterministic probabilistic behaviours which can preserve a compositionality of the parallel operator in the event structures and the calculus. We show an operational correspondence between the two semantics. This allows us to prove a “probabilistic confluence” result, which generalises the confluence of the linearly typed π-calculus.     

Quadratic optimal neural fuzzy control for synchronization of uncertain chaotic systems

This paper presents a novel quadratic optimal neural fuzzy control for synchronization of uncertain chaotic systems via H^∞ approach. In the proposed algorithm, a self-constructing neural fuzzy network (SCNFN) is developed with both structure and parameter learning phases, so that the number of fuzzy rules and network parameters can be adaptively determined. Based on the SCNFN, an uncertainty observer is first introduced to watch compound system uncertainties. Subsequently, an optimal NFN-based controller is designed to overcome the effects of unstructured uncertainty and approximation error by integrating the NFN identifier, linear optimal control and H^∞ approach as a whole. The adaptive tuning laws of network parameters are derived in the sense of quadratic stability technique and Lyapunov synthesis approach to ensure the network convergence and H^∞ synchronization performance. The merits of the proposed control scheme are not only that the conservative estimation of NFN approximation error bound is avoided but also that a suitable-sized neural structure is found to sufficiently approximate the system uncertainties. Simulation results are provided to verify the effectiveness and robustness of the proposed control method.     

The -basis and implicitization of a rational parametric surface

The concept of a μ-basis was introduced in the case of parametrized curves in 1998 and generalized to the case of rational ruled surfaces in 2001. The μ-basis can be used to recover the parametric equation as well as to derive the implicit equation of a rational curve or surface. Furthermore, it can be used for surface reparametrization and computation of singular points. In this paper, we generalize the notion of a μ-basis to an arbitrary rational parametric surface. We show that: (1) the μ-basis of a rational surface always exists, the geometric significance of which is that any rational surface can be expressed as the intersection of three moving planes without extraneous factors; (2) the μ-basis is in fact a basis of the moving plane module of the rational surface; and (3) the μ-basis is a basis of the corresponding moving surface ideal of the rational surface when the base points are local complete intersections. As a by-product, a new algorithm is presented for computing the implicit equation of a rational surface from the μ-basis. Examples provide evidence that the new algorithm is superior than the traditional algorithm based on direct computation of a Gröbner basis. Problems for further research are also discussed.     

Approximation by Bézier type of Meyer–König and Zeller operators

In this paper, we give direct, inverse and equivalence approximation theorems for the Bézier type of Meyer–König and Zeller operator with unified Ditzian–Totik modulus ω_φ^λ(f,t) (0≤λ≤1).     

On the representation of McCarthy's in the -calculus

We study the encoding of , the call-by-name λ-calculus enriched with McCarthy's amb operator, into the π-calculus. Semantically, amb is a challenging operator, for the fairness constraints that it expresses. We prove that, under a certain interpretation of divergence in the λ-calculus (weak divergence), a faithful encoding is impossible. However, with a different interpretation of divergence (strong divergence), the encoding is possible, and for this case we derive results and coinductive proof methods to reason about that are similar to those for the encoding of pure λ-calculi. We then use these methods to derive the most important laws concerning amb. We take bisimilarity as behavioural equivalence on the π-calculus, which sheds some light on the relationship between fairness and bisimilarity.     

Linearity and bisimulation

Exploiting linear type structure, we introduce a new theory of weak bisimilarity for the π-calculus in which we abstract away not only τ-actions but also non-τ actions which do not affect well-typed observers. This gives a congruence far larger than the standard bisimilarity while retaining semantic soundness. The framework is smoothly extendible to other settings involving nondeterminism and state. As an application we develop a behavioural theory of secrecy in the π-calculus which ensures secure information flow for a strictly greater set of processes than the type-based approach, while still offering compositional verification techniques.     

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.     

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.     

On the Expressiveness of Chi, Update, and Fusion calculi

Chi and Update calculi [9,17] have been independently introduced in order to model mobile systems. The two calculi are very close to each other and represent an evolution of π-calculus [15]. More recently a (non-straightforward) polyadic version of the Update calculus, the Fusion calculus, has been proposed [18].In the paper we give a fully abstract encoding from an asynchronous variant of Chi and Update calculi to asynchronous π-calculus [11,4]. This proves that, at least for their asynchronous variants, Chi and Update calculi are not more expressive than π-calculus. A similar result can be proved for the Fusion calculus.     

A -based optimal finite-word-length controller design

A novel optimal Finite Word Length (FWL) controller design is proposed in the framework of μ theory. A computationally tractable close-loop stability measure with FWL implementation considerations of the controller is derived based on the μ theory, and the optimal FWL controller realizations are obtained by solving the resulting optimal FWL realization problem using linear matrix inequality techniques.     

-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.     

Structured coalgebras and minimal HD-automata for the -calculus

The coalgebraic framework developed for the classical process algebras, and in particular its advantages concerning minimal realizations, does not fully apply to the π-calculus, due to the constraints on the freshly generated names that appear in the bisimulation.In this paper we propose to model the transition system of the π-calculus as a coalgebra on a category of name permutation algebras and to define its abstract semantics as the final coalgebra of such a category. We show that permutations are sufficient to represent in an explicit way fresh name generation, thus allowing for the definition of minimal realizations.We also link the coalgebraic semantics with a slightly improved version of history dependent (HD) automata, a model developed for verification purposes, where states have local names and transitions are decorated with names and name relations. HD-automata associated with agents with a bounded number of threads in their derivatives are finite and can be actually minimized. We show that the bisimulation relation in the coalgebraic context corresponds to the minimal HD-automaton.     

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.     

Delay-dependent robust stability and control for jump linear systems with delays

This paper considers robust stochastic stability, stabilization and H_∞ control problems for a class of jump linear systems with time delays. By using some zero equations, neither model transformation nor bounding for cross terms is required to obtain the delay-dependent results, which are given in terms of linear matrix inequalities (LMIs). Maximum sizes of time delays are also studied for system stability. Furthermore, solvability conditions and corresponding H_∞ control laws are given which provide robust stabilization with a prescribed H_∞ disturbance attenuation level. Numerical examples show that the proposed methods are much less conservative than existing results.     

A CPS Encoding of Name-Passing in Higher-Order Mobile Embedded Resources

We present an encoding of the synchronous π-calculus in the calculus of Higher-Order Mobile Embedded Resources (Homer), a pure higher-order calculus with mobile processes in nested locations, defined as a simple, conservative extension of the core process-passing subset of Thomsen's Plain CHOCS. We prove that our encoding is fully abstract with respect to barbed bisimulation and sound with respect to barbed congruence. Our encoding demonstrates that higher-order process-passing together with mobile resources in (local) named locations are sufficient to express π-calculus name-passing. The encoding uses a novel continuation passing style to facilitate the encoding of synchronous communication.     

Stability, robust stabilization and control of singular-impulsive systems via switching control

In this paper, stability, robust stabilization and H_∞ control of singular-impulsive systems are studied. Some new fundamental properties are derived for switched singular systems subject to impulse effects. Applying the Lyapunov function theory, several sufficient conditions are established for exponential stability, robust stabilization and H_∞ control of the corresponding singular-impulsive closed-loop systems. Some numerical examples are given to demonstrate the effectiveness of the proposed control and stabilization methods.     

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.     

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.