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In linear systems, designers use zeros for loop-shaping and the attenuation of disturbances. For example, imaginary-axis zeros can be used to reject sinusoids at a specific frequency such as a 50 Hz or 60 Hz power line interference. If the disturbance is nonsinusoidal, repetitive control methods may be used but additional controller states for each harmonic are required. Thus, rejecting periodic disturbance that are nonsinusoidal with low controller order remains an open problem. In this paper, we constructively design low-order nonlinear dynamics that reject a nonsinusoidal disturbance. We identify a particular case of the nonlinear regulator theory wherein the Byrnes--Isidori PDE has a simple solution. This case leads to a constructive procedure for designing nonlinear zero dynamics in systems with input disturbances. The constructive procedure is accessible to designers who do not have experience with the nonlinear geometric control theory. [DOI: 10.111511.3117187] Keywords: nonlinear geometric control, nonlinear zeros, regulator, notch filter

This technical note states new sufficient conditions for the exponential stability of linear time-varying (LTV) systems of the form [??] (x) = A(t)x(t). The approach proposed derives and uses the notion of perturbed frozen time (PFT) form that can be associated to any LTV system. Exploiting the Bellman-Gronwall lemma, relaxed stability conditions are then stated in terms of "average" parameter variations. Salient features of the approach are: pointwise stability of A (x) is not required, [absolute value of [??](x)] may not be bounded, the stability conditions also apply to uncertain systems. The approach is illustrated by numerical examples. Index Terms--Linear systems, stability conditions, time-varying systems.

This paper deals with the problems of regular implementability and stabilization of a given plant in the context of finite-dimensional linear differential system behaviors. In particular we solve the problems of regular implementability and stabilization using controllers in which a pre-specified subset of the plant control variables is free. We will also extend the results to the situation in which the set of plant control variables is partitioned into two complementary subsets. Variables from one subset should become controller inputs, while variables from the other should become controller outputs. In other words, we consider the problems of regular implementability and stabilization using controllers with a priori given input/output structure. Index Terms--Behaviors, input/outout structure, interconnection, linear systems, regular implementability, stabilization.

This note addresses the problem of synchronized output regulation of linear networked system where all the nodes have their outputs track signals produced by the same exosystem and the state of exosystem is accessible only to leader nodes, while follower nodes regulate their outputs via a distributed synchronous protocol. This problem can be decoupled into two: one is the output regulation problem on the synchronous manifold and the other is the stability problem of synchronous manifold. The proposed synchronous protocol is independent of the network topology. The stability of synchronous manifold is analyzed through the permissible eigenvalue region and the requirements of information graph. Finally, a numerical example illustrates the efficacy of the presented results. Index Terms--Information graph, networked systems, synchronized output regulation.

In this paper, we address the problem of robust stabilization and disturbance rejection for a class of hybrid linear systems subject to exponential uncertainties. By using Taylor series approximation and convex polytope technique, the exponentially uncertain hybrid linear system is transformed into an equivalent hybrid polytopic model subject to norm bounded uncertainty. For such equivalent hybrid linear model, we design its switching strategy and associated state feedback controllers so that such model is asymptotically stable with [H.sub.[infinity]] disturbance attenuation based on multiple Lyapunov function technology and linear matrix inequality (LMI) approach. [DOI: 10.1115/1.3072158] Keywords: hybrid linear systems, exponential uncertainty, disturbance rejection, convex polytope, LMIs

This technical note studies quantized output feedback control of discrete-time linear systems using a finite-level quantizer. The main objective is to find a quantization strategy which is easily implementable and achieves asymptotic stabilization. Based on a known logarithmic quantization scheme, we introduce a simple dynamic scaling method for the quantizer. A suboptimal approach for the optimization of the number of quantization levels and the design of a corresponding quantized dynamic output feedback controller is given. The robustness of the dynamic quantization scheme with respect to input disturbances is also examined. Index Terms--Linear time-invariant (LTI), single-input single-output (SISO).

We consider filter design of a linear system with parameter uncertainty. In contrast to the robust Kalman filter which focuses on a worst case analysis, we propose a design methodology based on iteratively solving a tradeoff problem between nominal performance and robustness to the uncertainty. Our proposed filter can be computed online efficiently, is steady-state stable, and is less conservative than the robust filter. Index Terms--Kalman filter, robust, tradeoff.

We consider the problem of designing a control law for a constrained linear system with bounded disturbances that ensures constraint satisfaction over an infinite horizon, while also guaranteeing that the closed-loop system has bounded [l.sub.2] gain. To this end, we propose a receding horizon control strategy based on the repeated calculation of optimal finite horizon feedback policies. We parameterize these policies such that the input at each time is an affine function of current and prior states, and minimize a worst-case quadratic cost where the disturbance energy is negatively weighted as in [H.sub.[infinity]] control. We show that the resulting receding horizon controller has two advantages over previous results for this problem. First, the policy optimization problem to be solved at each time step can be rendered convex-concave, with a number of decision variables and constraints that grows polynomially with the problem size, thereby making its solution amenable to standard techniques in convex optimization. Second, the achievable [l.sub.2] gain of the resulting closed-loop system is bounded and non-increasing with increasing control horizon. A numerical example is included to demonstrate the improvement in achievable [l.sub.2] gain relative to existing methods. Index Terms--Constrained systems, receding horizon control (RHC), robust control, robust optimization, uncertain systems.

This paper addresses robust performance analysis problems of linear time-invariant (LTI) systems affected by real parametric uncertainties. These problems, known also as a special class of structured singular value computation problems, are inherently intractable (NP-hard problems). As such intensive research effort has been made to obtain computationally tractable and less conservative analysis conditions, where linear matrix inequality (LMI) plays an important. Nevertheless, since LMI-based conditions are expected to be conservative in general, it is often the case that we cannot conclude anything if the LMI at hand turns out to be infeasible. This motivates us to consider the dual of the LMI and examine the structure of the dual solution. By pursuing this direction, in this paper, we provide rank conditions on the dual solution matrix under which we can conclude that the underlying robust performance is never attained. In particular, a set of uncertain parameters that violates the specified performance can be computed. These results come from block-moment matrix structure of the dual variable, which is consistent with the recent results on polynomial optimization. This particular structure enables us to make good use of simultaneous diagonalizability property of commuting diagonalizable matrices so that the sound rank conditions for the exactness verification can be obtained. Index Terms--Block-Moment matrix structure, dual linear matrix inequalities (LMIs), exactness verification, robust performance analysis.

We consider planar bilinear control systems with measurable controls. We show that any point in the reachable set can be reached by a "nice" control, specifically, a control that is a concatenation of a bang arc with either 1) a bang-bang control that is periodic after the third switch; or 2) a piecewise constant control with no more than two discontinuities. Under the additional assumption that the bilinear system is positive (or invariant for any proper cone), we show that the reachable set is spanned by a concatenation of a bang arc with either 1) a bang-bang control with no more than two discontinuities; or 2) a piecewise constant control with no more than two discontinuities. In particular, any point in the reachable set can be reached using a piecewise-constant control with no more than three discontinuities. Several known results on the stability of planar linear switched systems under arbitrary switching follow as corollaries of our result. We demonstrate this with an example. Index Terms--Lie algebra, Lie brackets, maximum principle, Metzler matrices, optimal control, positive linear systems, stability under arbitrary switching, switched systems.

This paper investigates the problem of robust passive control for singular systems which contain structure uncertainties and time delay. Three types of controllers are considered, namely, state feedback controller, observer-based state feedback controller, and dynamic output feedback controller, and the controllers are constructed such that closed-loop systems are generalized quadratically stable and passive with dissipation n. Design procedures and the algorithm are given for obtaining the maximum dissipation, and at the same time, the maximum guaranteed dissipation controllers are proposed. Illustrative examples are presented to show the validity and applicability of the proposed methods. Index Terms--Dissipation, feedback, generalized quadratic stability, linear matrix inequality (LMI), passivity, singular systems, time-delay.

This paper investigates the design of guaranteed cost controllers for a class of linear systems with a state delay using a time-multiplied linear quadratic cost function. Based on delay-dependent and delay-independent stability criteria, guaranteed cost controllers can be constructed via solutions to linear matrix inequalities (LMIs) such that the resulting closed-loop system is stable and a specified time-multiplied linear integral-quadratic cost function has an upper bound. By the cone complementary linearization method, delay-dependent state feedback controllers can be derived in terms of LMIs. A numerical example is provided to demonstrate the effectiveness of the proposed method. Keywords: guaranteed cost control linear matrix inequality, delay systems

In this note, the stability analysis and stabilization problems for a class of discrete-time Markov jump linear systems with partially known transition probabilities and time-varying delays are investigated. The time-delay is considered to be time-varying and has a lower and upper bounds. The transition probabilities of the mode jumps are considered to be partially known, which relax the traditional assumption in Markov jump systems that all of them must be completely known a priori. Following the recent study on the class of systems, a monotonicity is further observed in concern of the conservatism of obtaining the maximal delay range due to the unknown elements in the transition probability matrix. Sufficient conditions for stochastic stability of the underlying systems are derived via the linear matrix inequality (LMI) formulation, and the design of the stabilizing controller is further given. A numerical example is used to illustrate the developed theory. Index Terms--Linear matrix inequality (LMI), Markov jump linear systems, stochastic stability and stabilization, time-varying delays, transition probabilities.

This paper is concerned with the problem of robust [H.sub.[infinity]] filtering for linear continuous-time systems with polytopic parameter uncertainties and time-varying delay in the state. We utilize the polynomially parameter-dependent idea to solve the robust [H.sub.[infinity]] filtering problem, with new linear matrix inequality conditions obtained for the existence of admissible filters. These conditions are developed based on homogeneous polynomially parameter-dependent matrices of arbitrary degree. The delay-dependence and polynomial parameter-dependence guarantee the proposed approach to be potentially less conservative, which is shown via a numerical example. Index Terms--[H.sub.[infinity]] filtering, linear matrix inequality (LMI), robust filtering, time-delay systems, uncertain systems.

There has been renewed interest in the use of polynomial and homogeneous polynomial Lyapunov functions for addressing stability and performance issues in systems and control theory. However, no condition is yet available to establish the convexity of these functions and the convexity of their sublevel sets, properties that can be useful in many applications. In this paper, new conditions for establishing these convexity properties arc proposed, which can be handled through convex linear matrix inequalities optimizations by means of sum-of-squares relaxations. Index Terms--Convexity, linear matrix inequality (LMI), Lyapunov function, polynomial, sublevel set.

In this note, a sufficient condition is derived for the stability of a spatially invariant distributed dynamical system, based on the geometrical structure of the null space of a matrix polynomial. This condition is less conservative than the available computationally feasible criteria. Moreover, using the idea of parameter dependent linear matrix inequalities, a necessary and sufficient condition is obtained. Both of these two conditions are expressed by LMIs. While the necessity of the latter is lost if the degree of the related matrix polynomials is small, its conservativeness can be sequentially reduced. Index Terms--Linear matrix inequality (LMI), multivariate matrix polynomial, parameter dependent LMI, spatially distributed dynamic system, stability.

In this note, we study the controllability and observability problem for a class of controlled switching impulsive systems. By proposing several formula of variation of parameters for this type of time-varying systems and employing the characteristic polynomial theory of matrix, we establish necessary and sufficient conditions for controllability and controlled observability with respect to a given switching time sequence. Specializing the obtained results to the case of time-invariant linear switching impulsive systems, we derive some simple algebraic criteria, which include the results reported in the literature for time-invariant linear switching systems, linear impulsive systems and classical linear systems. One example is worked out for illustration. Index Terms--Controllability, controlled observability, hybrid systems, switching impulsive systems, variation of parameters.

Jump Markov Linear Systems are convenient models for systems that exhibit both continuous dynamics and discrete mode changes. Estimating the hybrid discrete-continuous state of these systems is important for control and fault detection. Existing solutions for hybrid estimation approximate the belief state by maintaining a subset of the possible discrete mode sequences. This approximation can cause the estimator to lose track of the true mode sequence when the effects of discrete mode changes are subtle. In this paper, we present a method for active hybrid estimation, where control inputs can be designed to discriminate between possible mode sequences. By probing the system for the purposes of estimation, such a sequence of control inputs can greatly reduce the probability of losing the true mode sequence compared to a nominal control sequence. Furthermore, by using a constrained finite horizon optimization formulation, we are able to guarantee that a given control task is achieved, while optimally detecting the hybrid state. In order to achieve this, we present three main contributions. First, we develop a method by which a sequence of control inputs is designed in order to discriminate optimally between a finite number of linear dynamic system models. These control inputs minimize a novel, tractable upper bound on the probability of model selection error. Second, we extend this approach to develop an active estimation method for Jump Markov Linear Systems by relating the probability of model selection error to the probability of losing the true mode sequence. Finally, we make this method tractable using a principled pruning technique. Simulation results show that the new method applied to an aircraft fault detection problem significantly decreases the probability of a hybrid estimator losing the true mode sequence. Index Terms--Estimation, fault diagnosis, hybrid systems, switching systems.

A controller design methodology for linear continuous-time systems using a state observer is proposed. In particular, the objective is to smooth the discontinuity resulting from a piecewise linear control law previously proposed, which improves the convergence rate of systems under asymmetrically constrained control. The proposed method is based on the use of a non quadratic asymmetrical Lyapunov function. Both full-order observers and minimal order observers are considered to reconstruct the inaccessible state. The speed of convergence of the controlled system and the observer is improved, with smooth control vector components, that respect always the imposed asymmetric constraints. Index Terms--Asymmetric constrained control, convergence rate improvement, decay rate, linear systems, state observers.

In this paper, we study the Poincare recurrence phenomenon for linear dynamical systems, that is, linear systems whose trajectories return infinitely often to neighborhoods of their initial condition. Specifically, we provide several equivalent notions of Poincare recurrence and review sufficient conditions for nonlinear dynamical systems that ensure that the system exhibits Poincare recurrence. Furthermore, we establish necessary and sufficient conditions for Poincare recurrence in linear dynamical systems. In addition, we show that in the case of linear systems the absence of volume-preservation is equivalent to the absence of Poincare recurrence implying irreversibility of a dynamical system. Finally, we introduce the notion of output reversibility and show that in the case of linear systems, Poincare recurrence is a sufficient condition for output reversibility. Index Terms--Irreversibility, Lagrangian and Hamiltonian systems, output reversibility, Poincare recurrence, volume-preserving flows.

Characterization and control of stability of switched dynamical systems and differential inclusions have attracted significant attention in the recent past. The most of the current results for this problem are obtained by application of the Lyapunov function method which provides sufficient but frequently over conservative stability conditions. For planar systems, practically verifiable necessary and sufficient conditions are found only for switched systems with two subsystems. This paper provides explicit necessary and sufficient conditions for asymptotic stability of switched systems and differential inclusions with arbitrary number of subsystems; these conditions turned out to be identical for the both classes of systems. A precise upper bound for the number of switching points in a periodic solution, corresponding to the break of stability, is found. It is shown that, for a switched system, the break of stability may also occur on a solution with infinitely fast switching (chattering) between some two subsystems. Index Terms--Asymptotic stability, differential inclusion, necessary and sufficient conditions, switched plane system.

The paper deals with definitions of zeros and poles and their features in finite-dimensional linear continuous-time periodic (FDLCP) systems under a harmonic framework. More precisely, system and transfer zeros and poles in the harmonic wave-to-wave sense are defined on what we call the regularized harmonic system operators and the harmonic transfer operators of FDLCP systems by means of regularized determinants; then their composition and properties related to system structures are examined via the Floquet theory and controllability/observability decompositions of FDLCP systems. The study shows that under mild assumptions, the harmonic transfer operators of FDLCP systems are analytic and meromorphic, on which zeros and poles are well-defined. Basic zero/pole relationships are established, which are similar to their linear time-invariant counterparts and in particular explicate some interesting harmonic wave-to-wave behaviors of FDLCP systems. The results are significant in analysis and synthesis of FDLCP systems when the harmonic approach is adopted. Index Terms--Continuous-time periodic system, Floquet factorization, harmonic transfer operator, zero and pole.

This paper presents an optimal dynamic quantizer synthesis method for controlling linear time-invariant systems with discrete-valued input. The quantizers considered here include dynamic feedback mechanism, for which we find quantizer parameters such that the system composed of a given linear plant and the quantizer is an optimal approximation of the linear plant in terms of the input-output relation. First, the performance of an arbitrarily given dynamic quantizer is analyzed, where we derive a dosed form expression of the performance. Based on this result, it is shown that the quantizer design is reduced to a nonconvex optimization problem for which it is hard to obtain a solution in a direct way. We obtain a globally Optimal solution, however, by taking advantage of a special structure of the problem which allows us to relax the original nonconvex problem. The resulting problem is easy to solve, so we provide a design method based on linear programming and derive an optimal structure of the dynamic quantizers. Finally, the validity of the proposed method is demonstrated by numerical examples. Index Terms--Discrete-valued input, dynamic quantizers, hybrid systems, quantized systems.

In the paper, an extension of LaSalle's Invariance Principle to a class of switched linear systems is studied. One of the motivations is the consensus problem in multi-agent systems. Unlike most existing results in which each switching mode in the system needs to be asymptotically stable, this paper allows that the switching modes are only Lyapunov stable. Under certain ergodicity assumptions, an extension of LaSalle's Invariance Principle for global asymptotic stability is obtained. Then it is used to solve the consensus reaching problem of certain multi-agent systems in which each agent is modeled by a double integrator, and the associated interaction graph is switching and is assumed to be only jointly connected. Index Terms--LaSalle's invariance principle, multi-agent consensus, switched linear systems, weak common quadratic Lyapunov function.

In this note, we investigate the controllability of linear hybrid systems via bumpless transfer input and constrained switching. By bumpless transfer input, we mean that the control input signals are as close as possible at switching times. By constrained switching, we mean that the switching index sequence is cyclic and the switching time sequence is possibly with pre-assigned duration intervals. While the problem is well motivated in several practical situations, it is also theoretically interesting. A complete criterion for controllability is presented, and a computational procedure is developed for finding a switching signal and a control input to achieve the controllability. Index Terms--Bumpless transfer input, controllability, linear hybrid systems, switching signal.

This paper formulates and solves the network reconstruction problem for linear time-invariant systems. The problem is motivated from a variety of disciplines, but it has recently received considerable attention from the systems biology community in the study of chemical reaction networks. Here, we demonstrate that even when a transfer function can be identified perfectly from input-output data, not even Boolean reconstruction is possible, in general, without more information about the system. We then completely characterize this additional information that is essential for dynamical reconstruction without appeal to ad-hoc assumptions about the network, such as sparsity or minimality. Index Terms--Network reconstruction, networked systems, systems biology.

Robust dynamic output design most often relies on nonconvex problems. This is precisely the case with linear parameter-varying (LPV) control when the measured varying parameters do not exactly fit the real ones. This paper provides a solution in the convex programming framework with the use of linear matrix inequality (LMI) solvers in the case of poly-topic parameter dependence. A bounded uncertainty set is defined from the difference between the measured and the true parameters from which LMI stabilization and performance conditions are obtained after bounding. As a desired property, the proposed conditions reduce to the classical LPV ones whenever the true parameters are available for control synthesis. Index Terms--Linear matrix inequality (LMI), linear parameter-varying (LPV) control design, uncertain linear systems.

We study control problems for linear systems in the behavioral framework. Our focus is a class of regular controllers that are equivalent to the canonical controller. The canonical controller is a particular controller that is guaranteed to solve the control problem whenever a solution exists. However, it has been shown that, in most cases, the canonical controller is not regular. The main result of the note is a parametrization of all regular controllers that are equivalent to the canonical controller. The parametrization is then used to solve two control problems. The first problem is related to designing a regular controller that uses as few control variables as possible. The second problem is to design a regular controller that satisfies a predefined input-output partitioning constraint. In both problems, based on the parametrization, we present algorithms for designing the controllers. Index Terms--Behavior, canonical controller, input-output partition, regularity.

The problem of checking certain controllability properties of even very simple piecewise linear systems is known to be undecidable. This paper focuses on conewise linear systems, i.e., systems for which the state space is partitioned into conical regions and a linear dynamics is active on each of these regions. For this class of systems, we present algebraic necessary and sufficient conditions for controllability. We also show that the classical results of controllability of linear systems and input-constrained linear systems can be recovered from our main result. Our treatment employs tools both from geometric control theory and mathematical programming. Index Terms--Conewise linear systems, controllability, hybrid systems, piecewise linear systems, push-pull systems, reachability.

We consider a hinged elastic beam described by the Rayleigh beam equation on the interval [0, [pi]]. We assume the presence of two sensors: one measures the angular velocity of the beam at a point [xi] [member of] [0, [pi]] and the other measures the bending (curvature) of the beam at the same point. (If [xi] = 0 or [xi] : [pi], then the second output is not needed.) The corresponding operator semigroup is unitary on a suitable Hilbert state space. These two measurements are advantageous because they make the open-loop system exactly observable, regardless of the point [xi]. We design the actuators and the feedback law in order to exponentially stabilize this system. Using the theory of collocated static output feedback developed in our recent paper [6], we design the actuators such that they are collocated, meaning that B = C*, where B is the control operator and C is the observation operator. It turns out that if [member of] (0, [pi]), then the actuators cause a discontinuity of the bending exactly at [xi] (this is the price, in this example, of having collocated actuators and sensors). This obliges us to use an extension of C to define the output signal in terms of the left and right limit of the bending at [xi]. We prove that, for all static output feedback gains in a suitable finite range, the closed-loop system is well posed and exponentially stable. This follows from the general theory in our paper [6], whose main points are recalled here. Index Terms--Collocated sensors and actuators, exact controllability and observability, output feedback, Rayleigh beam, wellposed linear system.

During recent decades, controllability and observability of linear time delay systems have been studied, including various definitions and corresponding criteria. However, the lack of an analytical solution approach has limited the applicability of the existing theory. Recently, the solution to systems of linear delay differential equations has been derived in the form of an infinite series of modes written in terms of the matrix Lambert W function. The solution form enables one to put the results for point-wise controllability and observability of systems of delay differential equations to practical use. We derive the criteria for point-wise controllability and observability, obtain the analytical expressions for their Gramians in terms of the parameters of the system, and develop a method to approximate them for the first time using the matrix Lambert W function-based solution form. Index Terms--Controllability, delay differential equations, Gramian, matrix Lambert W function, observability.

This paper investigates the number of switchings and design of switching sequences for controllability of switched linear systems. Two related results are established. One is a new constructive approach to designing switching sequences. The controllable state set of each switching sequence designed via the approach coincides with the controllable subspace of switched linear systems. The other is a well-estimated value for the minimum number of switchings required for controllability. Each state in the controllable subspace can be steered to origin within this value of switching times. Index Terms--Constructive method, controllability, hybrid systems, reachability, switched systems, switching sequence.

This paper is devoted to stability analysis and control design of switched linear systems in both continuous and discrete-time domains. A particular class of matrix inequalities, the so-called Lyapunov--Metzler inequalities, provides conditions for open-loop stability analysis and closed-loop switching control using state and output feedback. Switched linear systems are analyzed in a general framework by introducing a quadratic in the state cost determined from a series of impulse perturbations. Lower bounds on the cost associated with the optimal switching control strategy are derived from the determination of a feasible solution to the Hamilton--Jacobi--Bellman inequality. An upper bound on the optimal cost associated with a closed-loop stabilizing switching strategy is provided as well. The solution of the output feedback problem is based on the construction of a full-order linear switched filter whose state variable is used by the mechanism for the determination of the switching rule. Throughout, the theoretical results are illustrated by means of academic examples. A realistic practical application related to the optimal control of semiactive suspensions in road vehicles is reported. Index Terms--Linear matrix inequalities (LMIs), output feedback control, switched systems.

This paper extends results from [D. Liberzon and D. Nesic, "Input-to-state stabilization of linear systems with quantized feedback," IEEE Trans. Autom. Control, vol. 52, no. 5, pp. 767-781, May 2007], where input-to-state stabilization (ISS) of linear systems with quantized feedback was considered. In this paper, we show that, by using the same scheme and under the same conditions as in D. Liberzon and D. Nesic, "Input-to-state stabilization of linear systems with quantized feedback," IEEE Trans. Autom. Control, vol. 52, no. 5, pp. 767-781, May 2007, it is also possible to achieve (nonlinear gain) [l.sub.2] stabilization for linear systems. We also prove a new lemma on [[kappa].sub.[infinity]] functions that is interesting in its own right. Index Terms--Disturbances, [l.sub.2] stabilization, quantized feedback.

We consider the following problem: given a linear system and a linear temporal logic (LTL) formula over a set of linear predicates in its state variables, find a feedback control law with polyhedral bounds and a set of initial states so that all trajectories of the closed loop system satisfy the formula. Our solution to this problem consists of three main steps. First, we partition the state space in accordance with the predicates in the formula, and construct a transition system over the partition quotient, which captures our capability of designing controllers. Second, using a procedure resembling model checking, we determine runs of the transition system satisfying the formula. Third, we generate the control strategy. Illustrative examples are included. Index Terms--Control, model checking, temporal logic, transition systems.

In this note, we establish a set of conditions under which an ellipsoid is contractively invariant with respect to a singular linear system under a saturated linear feedback. These conditions can be expressed in terms of linear matrix inequalities, and the largest contractively invariant ellipsoid can be determined by solving an optimization problem with LMI constraints. With the feedback gain viewed as an additional variable, this optimization problem can be readily adapted for the design of feedback gain that results in the largest contractively invariant ellipsoid. Moreover, in the degenerate case where the singular linear system reduces to a regular system, our set invariance conditions reduce to the existing set invariance conditions for normal linear systems. Index Terms--Actuator saturation, set invariance, singular systems.

By using a delay line as a signal generator, we design a simple robust controller for the approximate regulation (i.e., approximate asymptotic tracking and rejection) of almost periodic signals for linear systems. As opposed to the related existing results, our controller design does not require online parameter tuning. Besides the usual assumptions about stabilizability, detectability, and nonexistence of transmission zeros for the plant, the controller design algorithm of this paper only requires knowledge of the desired tracking accuracy [member of ] > 0. Based on this information alone, we can only design a robust controller achieving, in the presence of unknown trigonometric polynomial disturbances and additive perturbations to the plant and the controller, [lim sup.sub.[right arrow] [infinity]] [parallel] y(t) - [y.sub.ref] (t) [parallel] < [member of] [parallel] [y.sub.ref] [parallel]. Here, y is the output of the plant and [y.sub.ref] is an arbitrary almost periodic reference signal taken from an infinite-dimensional generalized Sobolev space of almost periodic functions. In this paper, we also study robust output regulation in the limiting case where [member of] [right arrow] O. It turns out that, due to the general loss of exponential closed loop stability, asymptotic tracking/rejection can also be lost as [member of] [right arrow] 0, unless the exogenous signals are smooth enough. This last result extends some recent theorems on (nonrobust) open loop output regulation for infinite-dimensional exosystems. The results of this paper are new and potentially useful for finite-dimensional plants, but the main results are also true for infinite-dimensional systems with bounded control and observation operators. Index Terms--Linear systems, periodic control, periodic functions, regulators, robustness.

Under the assumption that the regulation error is the only feedback signal, it is shown how to design a global regulator capable of rejecting and/or tracking signals made of at most m sinusoidal terms with unknown frequencies, magnitudes, and phases for linear observable minimum phase systems. The asymptotic convergence of the tracking error to zero is guaranteed provided that an upper bound is known on the number of sinusoidal terms, even though the values of the unknown frequencies may not be recovered. Exponential convergence is achieved if all the exosystem frequencies are excited. Index Terms--Linear systems, minimum phase, output regulation, unknown exosystem.

This paper is concerned with the stabilization of discrete-time linear systems with quantization of the input and output spaces, i.e., when available values of inputs and outputs are discrete. Unlike most of the existing literature, we assume that how the input and output spaces are quantized is a datum of the problem, rather than a degree of freedom in design. Our focus is hence on the existence and synthesis of symbolic feedback controllers, mapping output words into the input alphabet, to steer a quantized I/O system to within small invariant neighborhoods of the equilibrium starting from large attraction basins. We provide a detailed analysis of the practical stabilizability of systems in terms of the size of hypercubes bounding the initial conditions, the state transient, and the steady-state evolution. We also provide an explicit construction of a practically stabilizing controller for the quantized I/O case. Index Terms--Controlled invariance, dynamic output feedback, practical stability, quantized systems.

The present paper is concerned with the design of dynamic anti-integrator-windup controllers for critically stable linear systems with a single pole at the origin. The constant gain term in the conventional anti-windup controller is extended to have dynamics represented by a transfer function. The proposed dynamic anti-windup compensator is similar to the one based on co-prime factorization of the plant. The overall controller includes an internal model for constant signals and achieves regulation for constant disturbance and reference inputs as long as the asymptotic control input stays within the saturation limits. The effectiveness of the proposed method is demonstrated on a one-link flexible arm through simulations and experiments. [DOI: 10.1115/1.2397146] Keywords: input constraints, dynamic controller, anti-windup compensator, Lyapunov design, flexible mechanical arm, mechatronic systems

This paper presents a novel compensator segmentation scheme for rule-based control of a linear system characterized by structured uncertainties. To start with, it is assumed that the design of a segmented compensator becomes necessary because the parameter variation region is too wide to be handled by a single robust compensator. The segmentation scheme is based on the simulated annealing technique. Starting with an initial estimate of the number of segments, the off-line segmentation scheme attempts to minimize it while assuring coverage of the entire parameter variation region. The information about the segment boundaries and the appropriate compensators is then utilized as the database of a rule-based switching controller. The paper includes the results of simulation studies that demonstrate the performance of the proposed scheme.

Most realistic control problems involve some type of constraint. However, to date, all the algorithms that deal with constrained problems assume that the system is perfectly known. On the other hand, during the last decade a considerable amount of time has been spent in the robust control problem. However, in its present form, the robust control theory can address only the idealized situation of completely unconstrained problems. In this note we present a theoretical framework to analyze the stability properties of constrained discrete-time systems under the presence of uncertainty and we show that this formalism provides a unifying approach, including as a particular case the well-known technique of estimating robustness bounds from the solution of a Lyapunov equation. These results are applied to the problem of designing feedback controllers capable of stabilizing a family of systems, while at the same time satisfying state-space constraints.

In this note, we deal with the problem of stabilizing a class of uncertain time-delay systems via memoryless linear feedback. The systems under consideration are linear systems with time-varying state delays. They also contain uncertain parameters (possibly time-varying) whose values are known only to within a prescribed compact bounding set. The main contribution given here is to enlarge the class of time-delay systems for which one can construct a stabilizing memoryless linear feedback controller. Within this framework, a new notion of robust memoryless stabilizability is first introduced via the method of Lyapunov functionals. Then a sufficient condition for the stabilizability is proposed. It is shown that solvability of a parametrized Riccati equation can be used to determine whether the time-delay system satisfies the sufficient condition. Furthermore, if there exists a positive definite symmetric solution satisfying the Riccati equation, a suitable memoryless linear feedback law can be derived also.

We consider n-dimensional positive linear switched systems. A necessary condition for stability under arbitrary switching is that every matrix in the convex hull of the matrices defining the subsystems is Hurwitz. Several researchers conjectured that for positive linear switched systems this condition is also sufficient. Recently, Gurvits, Shorten, and Mason showed that this conjecture is true for the case n = 2, but is not true in general. Their results imply that there exists some minimal integer [n.sub.p] such that the conjecture is true for all n < [n.sub.p], but is not true for n = [n.sub.p].We show that [n.sub.p] = 3. Index Terms--Metzler matrix, positive linear systems, stability under arbitrary switching law, switched systems.