Delay-dependent filtering for time-delayed LPV systems

The present paper addresses the parameter-dependent filter design problem for output estimation in linear parameter varying (LPV) plants that include constant delays in the state. We develop LMI-based delay-dependent conditions to guarantee stability and an induced gain bound performance for the filtering error system. An explicit characterization of the filters’ state–space representation is given in terms of the solutions to a convex optimization problem associated with the synthesis conditions. By taking the output estimation error into account as the criterion, the developed filters are shown to be capable of tracking the desired outputs of the time-delayed parameter varying system in the presence of external disturbances. Two families of filters are examined: memoryless and state-delayed filters. The latter one which involves a delay term in its dynamics has the benefit of reducing the conservatism in the design and improving performance. Illustrative examples are provided to demonstrate the feasibility and advantages of the proposed methodologies for memoryless and state-delayed filter design and to validate the superiority of using the state-delayed configuration compared to the conventional memoryless filters.     

Powers in a class of -strict standard episturmian words

This paper concerns a specific class of strict standard episturmian words whose directive words resemble those of characteristic Sturmian words. In particular, we explicitly determine all integer powers occurring in such infinite words, extending recent results of Damanik and Lenz [D. Damanik, D. Lenz, Powers in Sturmian sequences, European J. Combin. 24 (2003) 377–390, doi:10.1016/S0195-6698(03)00026-X], who studied powers in Sturmian words. The key tools in our analysis are canonical decompositions and a generalization of singular words, which were originally defined for the ubiquitous Fibonacci word. Our main results are demonstrated via some examples, including the k-bonacci word, a generalization of the Fibonacci word to a k-letter alphabet (k≥2).     

An LMI approach to synthesis subject to almost asymptotic regulation constraints

A multi-objective controller synthesis problem is considered in which an output is to be regulated approximately by assuring a bound on the steady-state peak amplification in response to an infinite-energy disturbance, while also guaranteeing a desired level of performance measured in terms of the worst-case energy gain from a finite-energy input to a performance output. Relying on a characterization of the controllers with which almost asymptotic regulation is accomplished, the problem of guaranteeing the desired level of performance is reduced to solving a system of linear matrix inequalities subject to a set of linear equality constraints. Based on the solution of this system, a procedure is outlined for the construction of a suitable controller whose order is equal to the order of the plant plus the order of the exogenous system.     

A simple derivation of ARE solutions to the standard control problem based on LMI solution

In this note, a simple derivation of the Riccati equation based solutions to the standard control problem, namely the well-known Glover–Doyle solution and DGKF solution is given based on LMI solution. It is hoped that this will be helpful in deepening the understanding of Riccati equation solutions.     

An LMI approach to boundary control of semilinear parabolic and hyperbolic systems

Exponential stability analysis and L₂-gain analysis are developed for scalar uncertain distributed parameter systems, governed by semilinear partial differential equations of parabolic and hyperbolic types. Sufficient exponential stability conditions with a given decay rate are derived in the form of Linear Matrix Inequalities (LMIs) for both systems. These conditions are then utilized to synthesize  static output feedback boundary controllers of the systems in question.     

Thermodynamic evaluation of Cu– system based on newly determined Gibbs energy of formation of

Thermodynamic evaluation of Cu–Cu₃P system has been conducted by applying subregular solution model with Gibbs energy of Cu₃P formation that was newly determined by means of triple Knudsen cell mass spectrometry. Both the calculated vapor pressure of phosphorus and phase diagram of Cu–P system are excellently consistent with the literature data in the composition range of Cu–Cu₃P, indicating that there is no significant thermodynamic inconsistency between the present work based on the Gibbs energy of Cu₃P formation determined and the literature data.     

Delay-dependent – filter design for stochastic time-delay systems

This paper is concerned with the problem of – filter design for a class of stochastic time-delay systems. A delay-dependent sufficient condition is presented, which guarantees the existence of a linear filter ensuring that the filtering error system is stochastically asymptotically stable and its – performance satisfies a prescribed level. A desired filter can be constructed by solving certain linear matrix inequalities. A numerical example is given to demonstrate the effectiveness of the proposed method.     

An algorithm to generate all upper boundary points for in terms of minimal cuts

This paper discusses a stochastic-flow network from single-commodity case to multicommodity case. We propose a performance index, namely the probability that the upper bound of the system capacity is a given vector subject to the budget constraint, to evaluate the quality level for such a network. A simple approach based on minimal cuts is presented to generate the all upper boundary points for the demand subject to the budget B in order to evaluate the performance index.     

Dynamics of the difference equation

We study the invariant interval, the character of semicycles, the global stability, and the boundedness of the difference equation

where the initial conditions x_−k,…,x₋₁,x₀ are nonnegative, and p,q>0.     

Correlation of solubilities for the system with the Pitzer model at 15, 25, 50, and

Solubility data of the NaCl+LiCl+H₂O system have been measured at 15 C. These data along with others recorded in the literature, at 25, 50, and 100 C, have been correlated using the Pitzer model and the extended Debye–Hückel model. The latter was used to determine the activity and osmotic coefficients of the binary systems NaCl+H₂O and LiCl+H₂O. The results obtained in this work show that the calculated solubility values are in good agreement with the experimental ones.     

Fitting finite mixtures of generalized linear regressions in R

R package flexmix provides flexible modelling of finite mixtures of regression models using the EM algorithm. Several new features of the software such as fixed and nested varying effects for mixtures of generalized linear models and multinomial regression for a priori probabilities given concomitant variables are introduced. The use of the software in addition to model selection is demonstrated on a logistic regression example.     

Eventual regularity of the semigroup associated with the mono-tubular heat exchanger equation with output feedback

This paper is concerned with the regularity of the mono-tubular heat exchanger equation with output feedback. By approach of spectrum analysis, it is shown that the semigroup generated by the closed-loop operator consisting of the mono-tubular heat exchanger equation and the output feedback law is eventually differentiable and eventually compact.     

Robustness issues in optimal control of unstable plants

This paper presents a robustness analysis of the optimal solution of the step tracking problem in a one-degree of freedom control architecture, for the discrete-time multivariable (MIMO) case. It is shown that the resulting closed loop becomes arbitrarily fragile, i.e. the sensitivity peak becomes arbitrarily large, for certain reference directions. The cause of this problem is that the optimal controller depends on the reference direction. The paper shows that this dependence can be eliminated with an alternative formulation of the optimal problem where the cost is averaged over all reference directions.