Reachability analysis of reversal-bounded automata on series–parallel graphs

Acta Informatica - Extensions to finite-state automata on strings, such as multi-head automata or multi-counter automata, have been successfully used to encode many infinite-state non-regular...     

Prescribed-time leader-following consensus of linear multi-agent systems by bounded linear time-varying protocols

This paper considers the prescribed-time leader-following consensus problem of input-constrained linear multi-agent systems under generally directed communication topology in two cases:the Laplacian matrix related to the entire communication topology between agents is either known or unknown.In particular,the consensus problem for the former case is solved by a novel bounded linear time-varying(LTV) protocol,where the feedback gain is formulated by the parametric Lyapunov equation and the knowle...     

Stabilization of switched linear systems with bounded disturbances and unobservable switchings

This paper studies the stabilization problem of switched linear systems with bounded disturbances. It is assumed that the system switches among an infinite set of uniformly controllable linear systems, and that the switching signals are not observable, but the switching duration has a lower bound. It will be shown that by combining on-line adaptive estimation and control in the controller design, a feedback control law can be constructed which makes the switched linear system globally stable.     

On the size of Boyer–Moore automata

In this work we study the size of Boyer–Moore automata introduced in Knuth, Morris & Pratt’s famous paper on pattern matching. We experimentally show that a finite class of binary patterns produce very large Boyer–Moore automata, and find one particular case which we conjecture, generates automata of size Ω(m⁶)$\Omega \left(m^6\right)$. Further experimental results suggest that the maximal size could be a polynomial of O(m⁷)$O\left(m^7\right)$, or even an exponential O(2^0.4m)$O\left(2^{0.4m}\right)$, where m$m$ is the length of the pattern.     

Reachability analysis of switched linear discrete singular systems

This paper studies the reachability problem of the switched linear discrete singular （SLDS） systems. Under the condition that all subsystems are regular, the reachability of the SLDS systems is characterized based on a peculiar repeatedly introduced switching sequence. The necessary and sufficient conditions are obtained for the reachability of the SLDS systems.     

Stability and performance analysis of linear positive systems with delays using input–output methods

It is known that input–output approaches based on scaled small-gain theorems with constant D-scalings and integral linear constraints are non-conservative for the analysis of some classes of linear positive systems interconnected with uncertain linear operators. This dramatically contrasts with the case of general linear systems with delays where input–output approaches provide, in general, sufficient conditions only. Using these results, we provide simple alternative proofs for many of the existing results on the stability of linear positive systems with discrete/distributed/neutral time-invariant/-varying delays and linear difference equations. In particular, we give a simple proof for the characterisation of diagonal Riccati stability for systems with discrete-delays and generalise this equation to other types of delay systems. The fact that all those results can be reproved in a very simple way demonstrates the importance and the efficiency of the input–output framework for the analysis of linear positive systems. The approach is also used to derive performance results evaluated in terms of the L ₁-, L ₂- and L _∞-gains. It is also flexible enough to be used for design purposes.     

Stability analysis and design of fuzzy control system with bounded uncertain delays

Fuzzy control problems for systems with bounded uncertain delays were studied. Based on Lyapunov stability theory and matrix theory, a nonlinear state feedback fuzzy controller was designed by linear matrix inequalities （LMI） approach, and the global exponential stability of the closed-loop system was strictly proved. For a fuzzy control system with bounded uncertain delays, under the global exponential stability condition which is reduced to p linear matrix inequalities, the controller guarantees stability performances of state variables. Finally, the simulation shows the validity of the method in tiffs paper.     

Homotopy analysis method for solving multi-term linear and nonlinear diffusion–wave equations of fractional order

In this paper we have used the homotopy analysis method (HAM) to obtain solutions of multi-term linear and nonlinear diffusion–wave equations of fractional order. The fractional derivative is described in the Caputo sense. Some illustrative examples have been presented.     

Liouvillian solutions of linear difference–differential equations

For a field k$k$ with an automorphism σ$\sigma$ and a derivation δ$\delta$, we introduce the notion of Liouvillian solutions of linear difference–differential systems {σ(Y)=AY,δ(Y)=BY}$\{\sigma \left(Y\right)=AY,\delta \left(Y\right)=BY\}$ over k$k$ and characterize the existence of Liouvillian solutions in terms of the Galois group of the systems. In the forthcoming paper, we will propose an algorithm for deciding if linear difference–differential systems of prime order have Liouvillian solutions.