Linear Type System Research Articles

On the design of observer-based controller of linear neutral delay-differential systems

In this note, the observer-based control problem for a class of linear delay-differential systems of neutral type is investigated. Using the Lyapunov method, a criterion for asymptotic stability is derived in terms of matrix inequalities, which solved by convex optimization algorithms. A numerical example is given to illustrate the proposed method.

Linear types and non-size-increasing polynomial time computation

We propose a linear type system with recursion operators for inductive datatypes which ensures that all definable functions are polynomial time computable. The system improves upon previous such systems in that recursive definitions can be arbitrarily nested; in particular, no predicativity or modality restrictions are made.

A Theorem on Multiplicators in Nonhomogeneous Hölder Spaces and Some of Its Applications

In Sec. 2, sufficient conditions of the boundedness of convolution operators with kernel m in a nonhomogeneous Holder space are given in terms of the Fourier-image of m. After that, the results of Sec. 2 are used to prove the solvability in a Holder space of the Cauchy problem for linear systems of the hydrodynamic type. Bibliography: 6 titles.

Robust guaranteed cost control for uncertain linear differential systems of neutral type

In this paper, the robust guaranteed cost control problem for a class of uncertain linear differential systems of neutral type with a given quadratic cost functions is investigated. The uncertainty is assumed to be norm-bounded and time-varying nonlinear. The problem is to design a state feedback control laws such that the closed-loop system is robustly stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainty and time delay. A criterion for the existence of such controllers is derived based on the matrix inequality approach combined with the Lyapunov method. A parameterized characterization of the robust guaranteed cost controllers is given in terms of the feasible solutions to the certain matrix inequalities. A numerical example is given to illustrate the proposed method.

Flow-sensitive type qualifiers

We present a system for extending standard type systems with flow-sensitive type qualifiers. Users annotate their programs with type qualifiers, and inference checks that the annotations are correct. In our system only the type qualifiers are modeled flow-sensitively---the underlying standard types are unchanged, which allows us to obtain an efficient constraint-based inference algorithm that integrates flow-insensitive alias analysis, effect inference, and ideas from linear type systems to support strong updates. We demonstrate the usefulness of flow-sensitive type qualifiers by finding a number of new locking bugs in the Linux kernel.

A DISCRETIZED LYAPUNOV FUNCTIONAL APPROACH TO STABILITY OF LINEAR DELAY-DIFFERENTIAL SYSTEMS OF NEUTRAL TYPE

This paper considers the stability problem of linear delay-differential systems of neutral type. A discretized Lyapunov functional approach is developed. The resulting stability criteria are formulated in the form of a linear matrix inequality. For nominal systems, the analytical results can be approached with fine discretization. For uncertain systems, the new approach is much less conservative. Numerical examples show significant improvement over approaches in the literature.

The Invertibility of Linear Stationary Systems of Neutral Type

The Invertibility of Linear Stationary Systems of Neutral Type

Incomplete orthogonalization preconditioners for solving large and dense linear systems which arise from Semidefinite Programming

There is a strong need for the fast solution of large and dense linear systems which arise from the interior-point method for solving Semidefinite Programming with its dual problem. Often direct methods are too expensive in terms of computer memory and CPU-time requirements, then the only alternative is to use iterative methods. Here, a class of incomplete orthogonalization preconditioners for the conjugate gradient method for solving this type of linear systems will be proposed. The efficient feature of the preconditioners will be confirmed by several numerical experiments.

On regions and linear types (extended abstract)

We explore how two different mechanisms for reasoning about state, linear typing and the type, region and effect discipline, complement one another in the design of a strongly typed functional programming language. The basis for our language is a simple lambda calculus containing first-class memory regions, which are explicitly passed as arguments to functions, returned as results and stored in user-defined data structures. In order to ensure appropriate memory safety properties, we draw upon the literature on linear type systems to help control access to and deallocation of regions. In fact, we use two different interpretations of linear types, one in which multiple-use values are freely copied and discarded and one in which multiple-use values are explicitly reference-counted, and show that both interpretations give rise to interesting invariants for manipulating regions. We also explore new programming paradigms that arise by mixing first-class regions and conventional linear data structures.

Delay-Dependent H∞ Output-Feedback Control of State-Delayed Systems

The output-feedback H∞ control problem is solved for continuous-time, linear, retarded and neutral type systems. A delay-dependent solution is obtained in terms of linear matrix inequalities (LMIs) by using a descriptor model transformation of the system and by applying Park's inequality for bounding cross terms. An output-feedback controller is found by solving two LMIs, one of which is associated with a descriptor time-delay 'innovation filter'. Numerical examples axe given which illustrate the effectiveness of the new theory.

New Lyapunov–Krasovskii functionals for stability of linear retarded and neutral type systems

A new (descriptor) model transformation and a corresponding Lyapunov–Krasovskii functional are introduced for stability analysis of systems with delays. Delay-dependent/delay-independent stability criteria are derived for linear retarded and neutral type systems with discrete and distributed delays. Conditions are given in terms of linear matrix inequalities and for the first time refer to neutral systems with discrete and distributed delays. The proposed criteria are less conservative than other existing criteria (for retarded type systems and neutral systems with discrete delays) since they are based on an equivalent model transformation and since they require bounds for fewer terms. Examples are given that illustrate advantages of our approach.

Type Reconstruction for Linear π-Calculus with I/O Subtyping

Powerful concurrency primitives in recent concurrent languages and thread libraries provide great flexibility about implementation of high-level features like concurrent objects. However, they are so low-level that they often make it difficult to check global correctness of programs or to perform nontrivial code optimization, such as elimination of redundant communication. In order to overcome those problems, advanced type systems for input-only/output-only channels and linear (use-once) channels have been recently studied, but the type reconstruction problem for those type systems remained open, and therefore, their applications to concurrent programming languages have been limited. In this paper, we develop type reconstruction algorithms for variants of Kobayashi, Pierce, and Turner's linear channel type system with Pierce and Sangiorgi's subtyping based on input-only/output-only channel types and prove correctness of the algorithms. To our knowledge, no complete type reconstruction algorithm has been previously known for those type systems. We have implemented one of the algorithms and incorporated it into the compiler of the concurrent language HACL . This paper also shows some experimental results on the algorithm and its application to compile-time optimizations.

Linearity and the pi-calculus

The economy and flexibility of the pi-calculus make it an attractive object of theoretical study and a clean basis for concurrent language design and implementation. However, such generality has a cost: encoding higher-level features like functional computation in pi-calculus throws away potentially useful information. We show how a linear type system can be used to recover important static information about a process's behavior. In particular, we can guarantee that two processes communicating over a linear channel cannot interfere with other communicating processes. After developing standard results such as soundness of typing, we focus on equivalences, adapting the standard notion of barbed bisimulation to the linear setting and showing how reductions on linear channels induce a useful “partial confluence” of process behaviors. For an extended example of the theory, we prove the validity of a tail-call optimization for higher-order functions represented as processes.

98/00999 Novel technological trends in the use of brown coals: Salyaev, I. V. Ugol' Ukr., 1996, (9), 2. (in Russian)

The problem of strong stabilizability of linear systems of neutral type is investigated. We are interested in the case when the system has an infinite sequence of eigenvalues with vanishing real parts. This is the case when the main part of the neutral equation is not assumed to be stable in the classical sense. We discuss the notion of regular strong stabilizability and present an approach to stabilize the system by regular linear controls. The method covers the case of multivariable control and is essentially based on the idea of infinite-dimensional pole assignment proposed in [G.M. Sklyar, A.V. Rezounenko, A theorem on the strong asymptotic stability and determination of stabilizing controls, C. R. Acad. Sci. Paris Ser. I Math. 333 (8) (2001) 807–812]. Our approach is based on the recent results on the Riesz basis of invariant finite-dimensional subspaces and strong stability for neutral type systems presented in [R. Rabah, G.M. Sklyar, A.V. Rezounenko, Stability analysis of neutral type systems in Hilbert space, J. Differential Equations 214 (2) (2005) 391–428].

98/00996 Development of the coal-processing industry of Ukraine: Sklyar, M. G. and Starovoit, A. G. Koks Khim. 1997, (1), 2–9. (in Russian)

The problem of strong stabilizability of linear systems of neutral type is investigated. We are interested in the case when the system has an infinite sequence of eigenvalues with vanishing real parts. This is the case when the main part of the neutral equation is not assumed to be stable in the classical sense. We discuss the notion of regular strong stabilizability and present an approach to stabilize the system by regular linear controls. The method covers the case of multivariable control and is essentially based on the idea of infinite-dimensional pole assignment proposed in [G.M. Sklyar, A.V. Rezounenko, A theorem on the strong asymptotic stability and determination of stabilizing controls, C. R. Acad. Sci. Paris Ser. I Math. 333 (8) (2001) 807–812]. Our approach is based on the recent results on the Riesz basis of invariant finite-dimensional subspaces and strong stability for neutral type systems presented in [R. Rabah, G.M. Sklyar, A.V. Rezounenko, Stability analysis of neutral type systems in Hilbert space, J. Differential Equations 214 (2) (2005) 391–428].

Delay-independent stabilization of uncertain linear systems of neutral type

In this paper, we show that a sufficient condition for the delay-independent stabilizability of linear delay systems, which had been obtained by Amemiya et al., is also valid for linear neutral systems with measurable state variables by a new differential-difference inequality.

Robustness of Feedback Control Systems of Parabolic Type against Perturbations to an Elliptic Operator

We study robustness (stiffness) of feedback stabilization schemes for linear control systems of parabolic type against perturbations. The perturbations, often interpreted as modeling errors of physical systems, enter both the principal part and the boundary condition of the elliptic differential operator, which causes the change of the domain of definition for the elliptic operator. It is shown that the stabilization scheme works effectively for slightly perturbed systems insofar as the perturbations are small in adequate topologies. A study of various fractional powers of perturbed elliptic operators is the key to the theory. Made also is a characterization of domains of fractional powers of an elliptic operator with a feedback boundary condition.

Lyapunov's functionals and related optimal problems for differential-difference systems

The optimal control of linear differential-difference systems of neutral type, with respect to quadratic performance criteria over an infinite time interval is treated. The linear differential-difference systems with delays in coordinates, derivatives, and control actions are considered. The Lyapunov-Bellman formalism is used to find the optimal solution. The global optimality of the solution follows from convexity of the set of admissible controls and of the cost functional, and linearity of the constraints. The computational procedure is based on considering the approximate optimal problem. A connection is established between the original and approximate optimal problems.

Proving memory management invariants for a language based on linear logic

We develop tools for the rigorous formulation and proof of properties of runtime management for a sample programming language based on a linear type system. Two semantics are diescribed, one at a level of observable results of computations and one describing linear connectives in terms of memory-management primitives. The two semantics are proven equivalent and the memory-management model is proven to satisfy fundamental correctness criteria for reference counts.

Some Problems of Qualitative Control Theory for Time-delay Systems

The problem of modal control is extensively considered here for linear stationary time-delay systems of neutral type. To solve this problem a new type of regulators containing both time delays and state derivatives is introduced. Effective condition for the modal control by action of such regulators is given for the complete information case. In order to stUdy the modal control problem for systems with incomplete information an analog of the well-known dynamic regulator proposed by Pearson for systems with no delay is used.