On asymptotic model matching

In this paper we consider the problem of asymptotic model matching, in which the objective is to force the plant to behave asymptotically like a reference model in response to an exogenous input. Conditions for solvability via a linear time-invariant controller are well known; here we prove that under a closed-loop causality constraint, moving to a nonlinear time-varying controller affords no reduction of these conditions. We explore the ramifications of this result to the (ideal) model reference adaptive control problem, demonstrating that (i) an upper bound on the plant relative degreemust be known, and (ii) the plant zeros in the closed right half-planemust lie in a finite set. We also derive a bound on the achievable asymptotic performance in the event that the solvability conditions fail to hold.Supported by the Natural Sciences and Engineering Research Council of Canada via a research grant.Supported by the Natural Sciences and Engineering Research Council of Canada under Grant A4396.     

Delay-dependent H ∞ controller design for linear neutral systems with discrete and distributed delays

This article considers the delay-dependent H _∞ control problem for linear neutral systems with both discrete and distributed delays. The problem we address is to design a state feedback controller such that the resulting closed-loop system is asymptotically stable and satisfies a prescribed H _∞ performance level. First, a delay-dependent sufficient condition for the solvability of the problem is obtained in terms of matrix inequalities. Then, by using the cone complementarity linearization approach, an H _∞ controller is developed based on the solvability condition. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed method.     

On the static H∞ control problem

The problem of existence of static controller in standard H_∞ control problem or, equivalently, solvability of a couple of Riccati inequalities with respect to the same Hermitian matrix is reduced to solvability of a single Riccati inequality. This inequality is presented in a form which is bilinear with respect to unknown parameters. In a special case the inequality is transformed to LMI.     

(A, B)-invariant and stabilizability subspaces, a frequency domain description

In a paper of E. Emre and the author a polynomial characterization for (A, B)-invariant subspaces is given. The characterization is used to give a frequency domain criterion for the solvability of the disturbance decoupling problem. In this paper a more elementary and simpler treatment is given. Furthermore, stabilizability subspaces are introduced, are given a frequency domain characterization and are used to solve design problems.     

Solvability conditions and design for synchronization of discrete‐time multiagent systems

This paper provides solvability conditions for state synchronization with homogeneous discrete‐time multiagent systems with a directed and weighted communication network under partial‐ or full‐state coupling. Our solvability conditions reveal that the synchronization problem is solvable for all possible, a priori given, set of graphs associated with a communication network only under the condition that the agents are at most weakly unstable (ie, agents have all eigenvalues in the closed unit disc). However, if an upper bound on the eigenvalues inside the unit disc of the row stochastic matrices associated with any graph in a given set of graphs is known, then one can achieve synchronization for a class of unstable agents. We provide protocol design for at most weakly unstable agents based on a direct eigenstructure assignment method and a standard H₂ discrete‐time algebraic Riccati equation. We also provide protocol design for strictly unstable agents (ie, agents have at least one eigenvalue outside the unit disc) based on the standard H₂ discrete‐time algebraic Riccati equation.     

Explicit constructions of global stabilization and nonlinear H∞ control laws for a class of nonminimum phase nonlinear multivariable systems

This paper investigates a global stabilization problem and a nonlinear H_∞ control problem for a class of nonminimum phase nonlinear multivariable systems. To avoid the complicated recursive design procedure, an asymptotic time‐scale and eigenstructure assignment method is adopted to construct the control laws for the stabilization problem and the nonlinear H_∞ control problem. A sufficient solvability condition is established onthe unstable zero dynamics of the system for global stabilization problem and nonlinear H_∞ control problem, respectively. Moreover, based on the sufficient solvability condition, an upper bound of the achievable L₂‐gain is estimated for the nonlinear H_∞ control problem. Copyright © 2007 John Wiley & Sons, Ltd.     

Sufficient and necessary conditions for the solvability of the state feedback regulation problem

In this paper, we discuss the state feedback output regulation problem (SFRP) for infinite‐dimensional linear control systems with infinite‐dimensional exosystems. Under the polynomial stabilizability assumption, sufficient and necessary conditions are given for the solvability of the SFRP. The solvability of this problem is characterized in terms of the solvability of a pair of linear regulator equations. An application of the solvability of the SFRP for polynomial stable SISO system is given. Copyright © 2013 John Wiley & Sons, Ltd.     

An extension of the theory of learning systems

Summary The author's inquiry [1] on learning systems is generalized in the following respects: The process of learning, instead of coming to an end when the learning goal has been reached, is supposed to last for ever, so that the above definitive learning as well as phenomena such as forgetting, re-learning, changing the goal etc. become describable.We take over the notion of semi-uniform solvability of a set of learning problems (2.2), but now (trivial cases excluded) the whole capacity of a learning system is never s. u. solvable. Finite such sets are. The notion of a solving-basis of some is introduced and we can state necessary conditions that possess such a basis (2.14), so that examples of sets without a basis can be provided. On the other hand, any s. u. solvable has as basis. The notion of uniform solvability (3.1) reinforces that of s. u. solvability, and there are given sufficient conditions for to be uniformly solvable (3.6). In some finite cases, s. u. solvability, existence of a basis and uniform solvability coincide (3.7–3.9). At last we give the construction for the weakest learning system solving a uniformly solvable problem set (3.12–3.19).Eine deutsche Fassung wurde am 30. Mai 1972 eingereicht.     

A linear matrix inequality approach to H∞ control

The continuous- and discrete-time H_∞ control problems are solved via elementary manipulations on linear matrix inequalities (LMI). Two interesting new features emerge through this approach: solvability conditions valid for both regular and singular problems, and an LMI-based parametrization of all H_∞-suboptimal controllers, including reduced-order controllers. The solvability conditions involve Riccati inequalities rather than the usual indefinite Riccati equations. Alternatively, these conditions can be expressed as a system of three LMIs. Efficient convex optimization techniques are available to solve this system. Moreover, its solutions parametrize the set of H_∞ controllers and bear important connections with the controller order and the closed-loop Lyapunov functions. Thanks to such connections, the LMI-based characterization of H_∞ controllers opens new perspectives for the refinement of H_∞ design. Applications to cancellation-free design and controller order reduction are discussed and illustrated by examples.     

H ∞ control for 2-D singular delayed systems

This article considers the problem of H _∞ control for two-dimensional (2-D) singular delayed systems in Roesser models. The problem to be addressed is the design of a state feedback controller such that the acceptability, internal stability and causality of the resulting closed-loop system is guaranteed and a prescribed H _∞ performance level is ensured. In terms of a linear matrix inequality (LMI), a sufficient condition for the solvability of the problem is obtained. A desired state feedback controller can be designed by solving a certain LMI. A numerical example is provided to demonstrate the application of the proposed method.     

Multiple Lyapunov functions approach to observer-based H ∞ control for switched systems

This article investigates the issue of H _∞ control for a class of continuous-time switched Lipschitz nonlinear systems. None of the individual subsystems is assumed to be stabilisable with H _∞ disturbance attenuation. Based on a generalised multiple Lyapunov functions (GMLFs) approach, which removes the nonincreasing requirement at switching points, a sufficient condition for the solvability of the H _∞ control problem under a state estimation-dependent switching law is presented. Observers, controllers and a switching law are simultaneously designed. As an extension, a sufficient condition for exponential stabilisability is also given.     

An impossibility about failure detectors in the iterated immediate snapshot model

The Iterated Immediate Snapshot model (IIS) is an asynchronous computation model where processes communicate through a sequence of one-shot Immediate Snapshot (IS) objects. It is known that this model is equivalent to the usual asynchronous read/write shared memory model, for wait-free task solvability. Its interest lies in the fact that its runs are more structured and easier to analyze than the runs in the shared memory model. As the IIS model and the shared memory model are equivalent for wait-free task solvability, a natural question is the following: Are they still equivalent for wait-free task solvability, when they are enriched with the same failure detector? The paper shows that the answer to this question is “no”.     

STOCHASTIC STABILIZATION AND H∞ CONTROL FOR DISCRETE JUMPING SYSTEMS WITH TIME DELAYS

In this paper, robust stochastic stabilization and H_∞ control for a class of uncertain discrete‐time linear systems with Markovian jumping parameters are considered. Based on a new bounded real lemma derived upon an inequality recently proposed, a new iterative state‐feedback controller design procedure for discrete time‐delay systems is presented. Sufficient conditions for stochastic stabilization are derived in the form of linear matrix inequalities (LMIs) based on an equivalent model transformation, and the corresponding H_∞ control law is given. Finally, numerical examples are given to illustrate the solvability of the problems and effectiveness of the results.     

H∞-control with measurement-feedback for Pritchard-Salamon systems

In this paper we extend the finite-dimensional results for the H_∞-control problem with measurement-feedback to a large class of infinite-dimensional systems, allowing for a certain type of unboundedness in the input and output operators (the Pritchard-Salamon class). The main result of the paper relates the solvability to the suboptimal H_∞-control problem to the existence of stabilizing solutions to certain operator Riccati equations. Furthermore, a characterization of all suboptimal controllers is given.     

On the reliable decentralised stabilisation of n MIMO systems

In this paper, we consider the problem of reliable decentralised stabilisation for n multi-input multi-output (MIMO) systems when some of the shared controllers among these systems are faulty, in the sense that they fail to operate properly due to subsystem (module) failures that may occur in actuators, sensors or controllers. Specifically, we present a design framework using a dilated linear matrix inequalities (LMIs) technique for deriving reliable stabilising state-feedback gains for all n MIMO systems; while a set of decentralised unknown disturbance observers (UDOs) that are shared by all n MIMO systems is used for extending the result to the output-feedback case. Moreover, a sufficient condition for the solvability of the set of decentralised UDOs is given in terms of a minimum-phase condition of each subsystem and a lower-bounding condition on the number of outputs of each channel. We also present a numerical example that illustrates the applicability of the proposed technique.     

Robust <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> DOF control for uncertain T-S fuzzy neutral systems

This paper investigates the problem of robust H _∞ dynamic output-feedback (DOF) control for a class of uncertain T-S fuzzy neutral systems with linear fractional parametric uncertainties. The aim is to design a full-order fuzzy DOF controller that ensures asymptotic stability of the closed-loop system and guarantees a prescribed H ^∞ performance level on disturbance attenuation for all admissible uncertainties. Based on the Lyapunov-Krasoviskii functional and the Barbalat lemma, delay-dependent sufficient conditions for the solvability of this problem are presented in terms of LMIs. Finally, a simulation example is provided to demonstrate the effectiveness and applicability of the proposed method.     

H∞ model reduction for discrete-time singular systems

This paper investigates the problem of H_∞ model reduction for linear discrete-time singular systems. Without decomposing the original system matrices, necessary and sufficient conditions for the solvability of this problem are obtained in terms of linear matrix inequalities (LMIs) and a coupling non-convex rank constraint set. When these conditions are feasible, an explicit parametrization of the desired reduced-order models is given. Particularly, a simple LMI condition without rank constraint is derived for the zeroth-order H_∞ approximation problem. Finally, an illustrative example is provided to demonstrate the applicability of the proposed approach.