Weighted control with ‐stability constraint for switched positive linear systems

This paper is concerned with the problem of control with ‐stability constraint for a class of switched positive linear systems. The ‐stability means that all the poles of each subsystem of the resultant closed‐loop system belong to a prescribed disk in the complex plane. A sufficient condition is derived for the existence of a set of state‐feedback controllers, which guarantees that the closed‐loop system is not only positive and exponentially stable with each subsystem ‐stable but also has a weighted performance for a class of switching signals with average dwell time greater than a certain positive constant. Both continuous‐time and discrete‐time cases are considered, and all of the obtained conditions are formulated in terms of linear matrix inequalities, whose solution also yields the desired controller gains and the corresponding minimal average dwell time. Numerical examples are given to illustrate the effectiveness of the presented approach.Copyright © 2012 John Wiley & Sons, Ltd.     

Dual approaches to strictly positive real controller synthesis with a performance using linear matrix inequalities

The synthesis of controllers that minimize a performance index subject to a strictly positive real (SPR) constraint is considered. Two controller synthesis methods are presented that are then combined into an iterative algorithm. Each method synthesizes optimal SPR controllers by posing a convex optimization problem where constraints are enforced via linear matrix inequalities. Additionally, each method fixes the controller state‐feedback gain matrix and finds an observer gain matrix such that an upper bound on the closed‐loop ‐norm is minimized and the controller is SPR. The first method retools the standard ‐optimal control problem by using a common Lyapunov matrix variable to satisfy both the criteria and the SPR constraint. The second method overcomes bilinear matrix inequality issues associated with the performance and the SPR constraint by employing a completing the square method and an overbounding technique. Both synthesis methods are used within an iterative scheme to find optimal SPR controllers in a sequential manner. Comparison of our synthesis methods to existing methods in the literature is presented. Copyright © 2012 John Wiley & Sons, Ltd.     

Remarks on the relationship between stability and internal stability of nonlinear systems

In this paper, we investigate the relationship between stability and internal stability of nonlinear systems. It is shown that under certain conditions, stability implies attractivity of the equilibrium and that local stability with finite gain implies local asymptotic stability of the origin. Copyright © 2012 John Wiley & Sons, Ltd.     

Stability control and recurrent switching rules

Recently, it has been enlightened the interest of a class of switching rules with good properties, which are called eventually periodic: more precisely, it has been proven that a finite family of linear vector fields of can be stabilized by means of eventually periodic switching rules provided that it is asymptotically controllable and satisfies an additional finite time controllability condition. Unfortunately, simple examples point out that in general, eventually periodic switching rules are not robust with respect to state measurement errors. In this paper, we introduce a new type of switching rules with improved robustness properties, which are called recurrent switching rules. They are subject to the construction of a finite sequence of complete cones Γ₁, … ,Γ_H of . We shown that, if a stabilizing eventually periodic switching rule for is known, then Γ₁, … ,Γ_H can be constructed in such a way that is stabilized by any recurrent switching rule subject to Γ₁, … ,Γ_H. Copyright © 2012 John Wiley & Sons, Ltd.     

Quantized filtering for Markovian jump LPV systems with intermittent measurements

This paper investigates the problem of quantized filtering for a class of discrete‐time linear parameter‐varying systems with Markovian switching under data missing. The measured output of the plant is quantized by a logarithmic mode‐independent quantizer. The data missing phenomenon is modeled by a stochastic variable. The purpose of the problem addressed is to design a full‐order filter such that the filtering error dynamics is stochastically stable and the prescribed noise attenuation level in the sense can be achieved. Sufficient conditions are derived for the existence of such filters in terms of parameterized linear matrix inequalities. Then the corresponding filter synthesis problem is transformed into a convex optimization problem that can be efficiently solved by using standard software packages. A simulation example is utilized to demonstrate the usefulness of the developed theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.     

Input‐output triggered control using ‐stability over finite horizons

This paper investigates stability of nonlinear control systems under intermittent information. Following recent results in the literature, we replace the traditional periodic paradigm, where the up‐to‐date information is transmitted and control laws are executed in a periodic fashion, with the event‐triggered paradigm. Building on the small gain theorem, we develop input–output triggered control algorithms yielding stable closed‐loop systems. In other words, based on the currently available (but outdated) measurements of the outputs and external inputs of a plant, a mechanism triggering when to obtain new measurements and update the control inputs is provided. Depending on the noise in the environment, the developed algorithm yields stable, asymptotically stable, and ‐stable (with bias) closed‐loop systems. Control loops are modeled as interconnections of hybrid systems for which novel results on ‐stability are presented. The prediction of a triggering event is achieved by employing ‐gains over a finite horizon. By resorting to convex programming, a method to compute ‐gains over a finite horizon is devised. Finally, our approach is successfully applied to a trajectory tracking problem for unicycles. Copyright © 2014 John Wiley & Sons, Ltd.     

A mixed numerical–analytical stable pseudo‐inversion method aimed at attaining an almost exact tracking

This paper considers the problem of computing the input u(t) of an internally asymptotically stable, possibly non‐minimum phase, linear, continuous time system Σ yielding a very accurate tracking of a pre‐specified desired output trajectory . The main purpose of the new approach proposed here is to alleviate some limitations that inherent the classical methods developed in the framework of the preview‐based stable inversion, which represents an important reference context for this class of control problems. In particular, the new method allows one to deal with arbitrary and possibly uncertain initial conditions and does not require a pre‐actuation. The desired output to be exactly tracked in steady state is here assumed to belong to the set of polynomials, exponential, and sinusoidal time functions. The desired transient response is specified to obtain a fast and smooth transition toward the steady‐state trajectory , without under and/or overshoot in the case of a set point reset. The transient control input u_t(t) is a priori assumed to be given by a piecewise polynomial function. Once has been specified, this allows the computation of the unknown u_t(t) as the approximate least squares solution of the Fredholm's integral equation corresponding to the explicit formula of the output forced response. The steady‐state input u_s(t) is analytically computed exploiting the steady‐state output response expressions for inputs belonging to the same set of . Copyright © 2013 John Wiley & Sons, Ltd.     

Dissipativity‐based asynchronous control of discrete‐time Markov jump systems with mixed time delays

This paper addresses the problem of dissipativity‐based asynchronous control for a class of discrete‐time Markov jump systems. A unified framework to design a controller for discrete‐time Markov jump systems with mixed time delays is proposed, which is fairly general and can be reduced to a synchronous controller or a mode‐independent controller. Based on a stochastic Lyapunov function approach, which fully utilizes available information of the system mode and the controller, a sufficient condition is established to ensure the stochastic stability and strictly ( , , ) dissipative performance of the resulting closed‐loop system. Finally, the effectiveness and validity of the proposed method are illustrated with a simulation example.     

H∞ model predictive control for constrained discrete‐time piecewise affine systems

This paper investigates stability analysis for piecewise affine (PWA) systems and specifically contributes a new robust model predictive control strategy for PWA systems in the presence of constraints on the states and inputs and with l₂ or norm‐bounded disturbances. The proposed controller is based on piecewise quadratic Lyapunov functions. The problem of minimization of the cost function for model predictive control design is changed to minimization of the worst case of the cost function. Then, this objective is reduced to minimization of a supremum of the cost function subject to a terminal inequality by considering the induced l₂‐norm. Finally, the predictive controller design problem is turned into a linear matrix inequality feasibility exercise with constraints on the input signal and state variables. It is shown that the closed‐loop system is asymptotically stable with guaranteed robust performance. The validity of the proposed method is verified through 3 well‐known examples of PWA systems. Simulation results are provided to show good convergence properties along with capability of the proposed controller to reject disturbances.     

Robust nonlinear H ∞ control based on the incremental gain

The incremental gain is proposed as an alternative to the usual gain for designing nonlinear H _∞ controllers. Considering a class of plants with Lipschitz nonlinearities and using linear matrix inequalities, a state feedback controller is designed such that the closed‐loop system is exponentially stable in the absence of disturbance inputs and has incremental gain less than or equal to a minimized number in the presence of disturbances as well as model uncertainties. Moreover, a norm‐wise robustness analysis of the proposed technique against nonlinear uncertainties has been accomplished. Our result is verified through stabilization of both certain and uncertain systems in an incremental sense and also input tracking of a chaotic plant. Copyright © 2014 John Wiley & Sons, Ltd.     

Mixed control of hidden Markov jump systems

In this work, we study the mixed control for Markov jump linear systems with hidden Markov parameters. The hidden Markov process is denoted by , where the nonobservable component θ(k) represents the mode of operation of the system, whereas represents the observable component provided by a detector. The goal is to obtain design techniques for mixed control problems, with the controllers depending only on the estimate , for problems formulated in 3 different forms: (i) minimizing an upper bound on the norm subject to a given restriction on the norm; (ii) minimizing an upper bound on the norm, while limiting the norm; and (iii) minimizing a weighted combination of upper bounds of both the and norms. We propose also new conditions for synthesizing robust controllers under parametric uncertainty in the detector probabilities and in the transition probabilities. The so‐called cluster case for the mixed control problem is also analyzed under the detector approach. The results are illustrated by means of 2 numerical examples.     

gain bounds for systems with sector bounded and slope‐restricted nonlinearities

This paper proposes a new method for calculating a bound on the gain of a system comprising a linear time invariant part and a static nonlinear part, which is odd, bounded, zero at zero and has a restriction on its slope. The nonlinear part is also assumed to be sector bounded, with the sector bound being (possibly) different from that implied by the slope restriction. The computation of the gain bound is found by solving a set of linear matrix inequalities, which arise from an integral quadratic constraint formulation of a multiplier problem involving both Zames‐Falb and Popov multipliers. Examples illustrate the effectiveness of the results, and comparisons are made against the state‐of‐the‐art. Copyright © 2011 John Wiley & Sons, Ltd.     

‐Gain analysis of event‐triggered networked control systems: a discontinuous Lyapunov functional approach

In this paper, the problems of exponential stability and ‐gain analysis of event‐triggered networked control systems (NCSs) with network‐induced delays are studied. We first propose event‐triggering conditions in the sensor side and controller side, respectively. Because the implementation of our event‐triggering scheme only needs periodic supervision of the system state at the constant sampling instants, instead of being monitored continuously, it is expected that the scheme will improve the resource utilization. Taking the network‐induced delays into account and using delay system approach, we constructed a unified model of NCSs with hybrid event‐triggering schemes. On the basis of this model, sufficient conditions for the exponential stability and ‐gain analysis are developed in the form of LMIs by using a discontinuous Lyapunov–Krasovskii functional approach. Moreover, the corresponding results can be further extended to more general cases, where the system matrices of the considered plant contain parameter uncertainties, represented in either polytopic or norm‐bounded frameworks. In addition, as a special case, we also present the exponential stability, ‐gain analysis, and the control feedback gain design of event‐triggered NCSs without considering the effects of network‐induced delays and event‐triggering condition in the controller side. Finally, a simulation example is provided to illustrate the usefulness and effectiveness of the proposed hybrid event‐triggering schemes.Copyright © 2012 John Wiley & Sons, Ltd.     

Distributed filtering in sensor networks with randomly occurring saturations and successive packet dropouts

This paper is concerned with the distributed filtering problem for a class of nonlinear systems with randomly occurring sensor saturations (ROSS) and successive packet dropouts in sensor networks. The issue of ROSS is brought up to account for the random nature of sensor saturations in a networked environment of sensors, and accordingly, a novel sensor model is proposed to describe both the ROSS and successive packet dropouts within a unified framework. Two sets of Bernoulli distributed white sequences are introduced to govern the random occurrences of the sensor saturations and successive packet dropouts. Through available output measurements from not only the individual sensor but also its neighboring sensors, a sufficient condition is established for the desired distributed filter to ensure that the filtering dynamics is exponentially mean‐square stable and the prescribed performance constraint is satisfied. The solution of the distributed filter gains is characterized by solving an auxiliary convex optimization problem. Finally, a simulation example is provided to show the effectiveness of the proposed filtering scheme. Copyright © 2013 John Wiley & Sons, Ltd.     

Multi‐equilibrium property of metabolic networks: MMN module

This paper studies the multi‐equilibrium property of the multiple substrates and multiple products with no inhibition (MMN) module. On the basis of the topological structure, a model for such module is established in the form of a set of nonlinear ordinary differential equations. It is shown that the injectivity of the MMN module is equivalent to the nonsingularity of Jacobian matrix of its rate function, and a necessary and sufficient condition for the injectivity is obtained by using the Hadamard product. For non‐injective MMN module, a sufficient condition for existence of multiple positive equilibria is provided by introducing the concept of input‐matrix. For a type of commonly encountered MMN module— ‐MMN module—a structure‐oriented criterion for judging its injectivity is given. For ‐MMN modules with some special structure, it is shown that there does not exist multiply equilibria and the equilibrium (if exists) is asymptotically stable. Examples and simulations are given to illustrate the results obtained. Copyright © 2012 John Wiley & Sons, Ltd.     

Links between different stabilities of switched homogeneous systems with delays and uncertainties

This paper addresses the links between three stabilities (attractivity, asymptotic stability, and exponential stability) of switched homogeneous systems with delays and uncertainties. A system has a certain property over a given set of switching signals if the property holds for all switching signals in . It is shown that a switched homogeneous system of degree one is exponentially stable over a given set of switching signals if it is attractive or asymptotically stable over the same set. The result is then applied to switched linear systems with delays and uncertainties. Finally, an example follows to show that ‘being over a given set of switching signals’ is necessary to guarantee the equivalence between different stabilities. Copyright © 2015 John Wiley & Sons, Ltd.     

A novel three‐dimensional guidance law implementation using only line‐of‐sight azimuths

A novel three‐dimensional guidance law using only line‐of‐sight azimuths based on input‐to‐state stability and robust nonlinear observer is proposed for interception of maneuvering targets. The proposed guidance law does not need any prior information of unknown bounded target maneuvers and uncertainties. Since in practice the line‐of‐sight rate is difficult for a pursuer to measure accurately, a nonlinear robust observer is introduced to estimate it. A three‐dimensional guidance law with bearing only measurement is obtained for interception of maneuvering targets. The presented algorithm is tested using computer simulations against a maneuvering target. Copyright © 2014 John Wiley & Sons, Ltd.     

and control design for polytopic continuous‐time Markov jump linear systems with uncertain transition rates

This paper investigates the problems of and state feedback control design for continuous‐time Markov jump linear systems. The matrices of each operation mode are supposed to be uncertain, belonging to a polytope, and the transition rate matrix is considered partly known. By appropriately modeling all the uncertain parameters in terms of a multi‐simplex domain, new design conditions are proposed, whose main advantage with respect to the existing ones is to allow the use of polynomially parameter‐dependent Lyapunov matrices to certify the mean square closed‐loop stability. Synthesis conditions are derived in terms of matrix inequalities with a scalar parameter. The conditions, which become LMIs for fixed values of the scalar, can cope with and state feedback control in both mode‐independent and mode‐dependent cases. Using polynomial Lyapunov matrices of larger degrees and performing a search for the scalar parameter, less conservative results in terms of guaranteed costs can be obtained through LMI relaxations. Numerical examples illustrate the advantages of the proposed conditions when compared with other techniques from the literature. Copyright © 2015 John Wiley & Sons, Ltd.     

filtering of nonlinear plants over networks

In this paper, we consider the filtering problem for Lipschitz systems in a networked environment. We assume that the measurements transmitted over the network are subject to quantization, uncertain delays and communication constraints. We first analytically demonstrate how each of the these issues affect the filtering problem. Second, we tackle the filter design as an optimization problem with LMI constraints. The optimization maximizes the Lipschitz constant and thus the region of attraction for which the filter is stable and an bound is satisfied by the error system. Copyright © 2013 John Wiley & Sons, Ltd.     

A new approach to constrained state estimation for discrete‐time linear systems with unknown inputs

This paper addresses the problem of estimating the state for a class of uncertain discrete‐time linear systems with constraints by using an optimization‐based approach. The proposed scheme uses the moving horizon estimation philosophy together with the game theoretical approach to the filtering to obtain a robust filter with constraint handling. The used approach is constructive since the proposed moving horizon estimator (MHE) results from an approximation of a type of full information estimator for uncertain discrete‐time linear systems, named in short ‐MHE and –full information estimator, respectively. Sufficient conditions for the stability of the ‐MHE are discussed for a class of uncertain discrete‐time linear systems with constraints. Finally, since the ‐MHE needs the solution of a complex minimax optimization problem at each sampling time, we propose an approximation to relax the optimization problem and hence to obtain a feasible numerical solution of the proposed filter. Simulation results show the effectiveness of the robust filter proposed.