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This paper is concerned with the problem of energy-to-peak stochastic stability (EPSS) of two-dimensional (2-D) Roesser systems in the presence of state time-varying delays and multiplicative noises. First, a scheme that ensures a 2-D stochastic time-delay system is stochastically stable with an attenuation performance is proposed. The scheme presented in this paper can be regarded as an extension of the Lyapunov–Krasovskii functional method for 2-D stochastic time-delay systems, focusing on the EPSS problem. The proposed scheme is then utilized to derive delay-dependent EPSS conditions in terms of tractable linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the derived stability conditions. [ABSTRACT FROM AUTHOR]

This paper deals with the certification problem for robust quadratic stability, robust state convergence, and robust quadratic performance of linear systems that exhibit bounded rates of variation in their parameters. We consider both continuous-time (CT) and discrete-time (DT) parameter-varying systems. In this paper, we provide a uniform method for this certification problem in both cases and we show that, contrary to what was claimed previously, the DT case requires a significantly different treatment compared to the existing CT results. In the established uniform approach, quadratic Lyapunov functions, which are affine in the parameter, are used to certify robust stability, robust convergence rates, and robust performance in terms of linear matrix inequality feasibility tests. To exemplify the procedure, we solve the certification problem for $\mathscr {L}_2$ -gain performance both in the CT and the DT cases. A numerical example is given to show that the proposed approach is less conservative than a method with slack variables. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of local stabilization of nonlinear polynomial control systems subject to time-varying input delay and polytopic parameter uncertainty. A linear matrix inequality approach based on the Lyapunov–Krasovskii theory is proposed for designing a nonlinear polynomial state feedback controller ensuring the robust local uniform asymptotic stability of the system origin along with an estimate of its region of attraction. Two convex optimization procedures are presented to compute a stabilizing controller ensuring either a maximized set of admissible initial states for given upper bounds on the delay and its variation rate or a maximized lower bound on the maximum admissible input delay considering a given set of admissible initial states. Numerical examples demonstrate the potentials of the proposed stabilization approach. [ABSTRACT FROM AUTHOR]

This paper proposes an approach for assessing the stability of feedback interconnections where one element is a static slope-restricted nonlinearity and the other element is a linear system. The approach is based on the use of Zames–Falb multipliers where the dynamic portion of the multiplier is chosen as an externally positive noncausal transfer function. By restricting attention to a subset of these multipliers, a set of pure linear matrix inequality conditions is obtained which requires no initial parameterization by the user. A useful byproduct of using externally positive systems is that the results are applicable to nonodd slope restricted nonlinearities, which is not the case for all classes of Zames–Falb multipliers. [ABSTRACT FROM AUTHOR]

Periodic event-triggered control (PETC) is an appealing paradigm for the implementation of controllers on platforms with limited communication resources, a typical example being networked control systems. In PETC, transmissions over the communication channel are triggered by an event generator, which depends solely on the available plant and controller data and is only evaluated at given sampling instants to enable its digital implementation. In this paper, we consider the general scenario, where the controller communicates with the plant via multiple decoupled networks. Each network may contain multiple nodes, in which case a dedicated protocol is used to schedule transmissions among these nodes. The transmission instants over the networks are asynchronous and generated by local event generators. At given sampling instants, the local event generator evaluates a rule, which only involves the measurements and the control inputs available locally, to decide whether a transmission is needed over the considered network. Following the emulation approach, we show how to design local triggering generators to ensure input-to-state stability and $\mathcal {L}_p$ stability for the overall system based on a continuous-time output-feedback controller that robustly stabilizes the network-free system. The method is applied to a class of Lipschitz nonlinear systems, for which we formulate the design conditions as linear matrix inequalities. The effectiveness of the scheme is illustrated via simulations of a nonlinear example. [ABSTRACT FROM AUTHOR]

We prove that if a homogeneous, continuously differentiable vector field is asymptotically stable, then it admits a Lyapunov function, which is the ratio of two polynomials (i.e., a rational function). We further show that when the vector field is polynomial, the Lyapunov inequalities on both the rational function and its derivative have sum of squares certificates and, hence, such a Lyapunov function can always be found by semidefinite programming. This generalizes the classical fact that an asymptotically stable linear system admits a quadratic Lyapunov function, which satisfies a certain linear matrix inequality. In addition to homogeneous vector fields, the result can be useful for showing local asymptotic stability of nonhomogeneous systems by proving asymptotic stability of their lowest order homogeneous component. This paper also includes some negative results: We show that in absence of homogeneity, globally asymptotically stable polynomial vector fields may fail to admit a global rational Lyapunov function, and in presence of homogeneity, the degree of the numerator of a rational Lyapunov function may need to be arbitrarily high (even for vector fields of fixed degree and dimension). On the other hand, we also give a family of homogeneous polynomial vector fields that admit a low-degree rational Lyapunov function but necessitate polynomial Lyapunov functions of arbitrarily high degree. This shows the potential benefits of working with rational Lyapunov functions, particularly as the ones whose existence we guarantee have structured denominators and are not more expensive to search for than polynomial ones. [ABSTRACT FROM AUTHOR]

Internal model control (IMC), which explicitly incorporates a plant model and a plant inverse model as its components, has an intuitive control structure and simple tuning procedure. Within the IMC structure, we propose composite adaptive IMC (CAIMC) which simultaneously identifies the plant and the plant inverse to minimize modeling errors and further reduce the tracking error. In this paper, the design procedure of CAIMC is generalized to an $n$ -th-order SISO plant. The main challenge in the generalization is to find an identification algorithm for an $n$ -th order system that satisfies the stability constraint, while assuring closed-loop stability. In the literature, stability-constrained identification has been formulated as a convex programming problem by re-parameterizing the constraint as a linear matrix inequality, but boundedness and continuity of the estimated parameters, which are critical for closed-loop stability of an adaptive control algorithm, are not guaranteed. We propose a modified stability-constrained identification method with established boundedness and continuity properties. Closed-loop stability and asymptotic performance of CAIMC are then established under proper conditions. The effectiveness of the proposed algorithm is demonstrated with an example. [ABSTRACT FROM AUTHOR]

This paper is concerned with stability analysis and synthesis for discrete-time linear systems with stochastic dynamics. Equivalence is first proved for three stability notions under some key assumptions on the randomness behind the systems. In particular, we use the assumption that the stochastic process determining the system dynamics is independent and identically distributed with respect to the discrete time. Then, a Lyapunov inequality condition is derived for stability in a necessary and sufficient sense. Although our Lyapunov inequality will involve decision variables contained in the expectation operation, an idea is provided to solve it as a standard linear matrix inequality; the idea also plays an important role in state feedback synthesis based on the Lyapunov inequality. Motivating numerical examples are further discussed as an application of our approach. [ABSTRACT FROM AUTHOR]

In this paper, the stability and $L_2$ -gain properties of linear impulsive delay systems with delayed impulses are studied. Commonly employed techniques, in which the delayed impulses are treated using Newton–Leibniz formula, may not be applicable to $L_2$ -gain analysis, since they make the disturbance input appear in the impulse part. In order to circumvent the difficulty, we first augment the considered system to a time-delay system with switching nondelayed impulses. Due to the absence of delayed impulses, this new approach has advantages in constructing Lyapunov functions and handling the effects of impulse delays on the system performance. Switching-based time-dependent Lyapunov functions are introduced to deal with the resultant switching impulses of the augmented system. Sufficient conditions for exponential stability and $L_2$ -gain properties are derived in terms of linear matrix inequalities. Numerical examples are provided to illustrate the efficiency of the new approach. [ABSTRACT FROM AUTHOR]

This note is devoted to study the stabilization problem of stochastic nonlinear delay systems with exogenous disturbances and the event-triggered feedback control. By introducing the notation of input-to-state practical stability and an event-triggered strategy, we establish the input-to-state practically exponential mean-square stability of the suggested system. Moreover, we investigate the stabilization result by designing the feedback gain matrix and the event-triggered feedback controller, which is expressed in terms of linear matrix inequalities. Also, the lower bounds of interexecution times by the proposed event-triggered control method are obtained. Finally, an example is given to show the effectiveness of the proposed method. Compared with a large number of results for discrete-time stochastic systems, only a few results have appeared on the event-triggered control for continuous-time stochastic systems. In particular, there have been no published papers on the event-triggered control for continuous-time stochastic delay systems. This note is a first try to fill the gap on the topic. [ABSTRACT FROM AUTHOR]

It is proved in this paper that the existence of suitable multiple Lyapunov functions is a necessary and sufficient condition for a discrete-time nonlinear switching system, with given switches digraph, to be globally asymptotically stable. The same result is provided for the input-to-state stability. The less is the number of edges in the switches digraph, the less is the number of inequalities that are involved in the provided necessary and sufficient Lyapunov conditions. [ABSTRACT FROM AUTHOR]

This paper considers the input-to-state stability (ISS) of time-varying switched systems with time delays, where the upper bound estimation for the operator of Lyapunov function (UBEOL) is assumed to be time varying and mode dependent. The ISS and integral ISS are investigated for time-varying switched systems with time delays by using the Lyapunov–Razumikhin and comparison theorem methods. Since the coefficient in the UBEOL is time varying and takes a positive/negative value, the subsystems consist of both ISS and non-ISS subsystems, simultaneously. It is shown that our presented results have wider applications than some existing works. Two examples, including one of the consensus for time-varying multiagent systems with cooperative and competitive protocols, are presented to demonstrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

Stability analysis of nonlinear singular systems, arising from differential algebraic equations, is addressed in this paper, exploiting the fact that it belongs to the class of Positvstellensatz problems. By means of the direct Lyapunov method and a variety of convex descriptor forms, sufficient conditions in terms of linear matrix inequalities are developed. Issues concerning proper initialization and simulation are also considered. Illustrative examples are provided. [ABSTRACT FROM AUTHOR]

This paper deals with the stabilization of the feasible equilibrium point of a special class of nonlinear quadratic systems known as Lotka–Volterra (LV) systems, in the presence of interval uncertainty via a fixed linear state feedback (FLSF). It is well known that for a linear time-invariant system with interval uncertainty, stability at the vertices of a polytope implies stability in the interior of the whole polytope. It has been shown that this idea can be extended to examine the stability of LV systems in the presence of interval uncertainty, recently. In fact, it has been proved that in spite of nonlinear nature of the system, stability at a special vertex guarantees stability at all other vertices, which makes it easier to check the stability of the whole uncertain system. A subtle use of this fact in stabilization of interval LV systems via FLSF leads to a sufficient condition in terms of linear matrix inequalities. Also, the proposed approach is extended to a wider class of LV systems with time-varying and state-dependent system matrices. The efficiency of the proposed scheme is shown through numerical examples and simulations. [ABSTRACT FROM AUTHOR]

In this paper, a time-varying observer for a linear continuous-time plant with asynchronous sampled measurements is proposed. The observer is contextualized in the hybrid systems framework providing an elegant setting for the proposed solution. In particular, some theoretical tools are provided, in terms of linear matrix inequalities (LMIs), certifying asymptotic stability of a certain compact set where the estimation error is zero. We consider sampled asynchronous measurements that occur at arbitrary times in a certain window with an upper and lower bound. The design procedure, that we propose for the selection of the time-varying gain, is based on a constructive algorithm that is guaranteed to find a solution to an infinite-dimensional LMI whenever a feasible solution exists. [ABSTRACT FROM AUTHOR]

In this note, we clarify the statement given in the above paper, claiming that the condition for state feedback stabilisation tends to necessity. Actually, it is possible to find examples for which the above-mentioned condition introduces a very weak conservatism and hence is not necessary. The source of the conservatism has been identified. Furthermore, we also realized that the condition could be substantially improved in terms of computation time. Therefore both the analysis and synthesis conditions are improved. [ABSTRACT FROM AUTHOR]

This paper deals with the exponential stabilization problem of discrete-time Markovian jump systems via a hybrid control strategy, in which the transition probability matrix and static output-feedback controller are designed simultaneously. A necessary and sufficient condition for the existence of an exponential stabilizing transition probability matrix is derived by means of a mode-dependent parametric approach. Furthermore, a sufficient condition is established for the above-mentioned hybrid design with a specified lower bound on the decay rate. The proposed design approaches can be applied to solve two kinds of control design problems with practical constraints imposed on the hybrid design. Besides, an estimation approach is proposed on the decay rate and decay coefficient of the jump systems. Also, two optimization problems are formulated to obtain the hybrid control strategy. Finally, two numerical examples and a network-on-chip based application are provided to illustrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

In this paper, tractable stability and performance conditions are presented for systems consisting of an infinite number of spatially invariant, i.e., identical subsystems that are described by (non)linear differential equations and interconnected (partly) through packet-based communication networks. These networks transmit packets asynchronously and independently of each other and are equipped with scheduling protocols that determine which actuator, sensor, or controller node is allowed access to the network. The overall system is modeled as an infinite interconnection of spatially invariant hybrid subsystems. To underline the relevance of this framework, it is shown how two well-known and natural system configurations can be captured in this hybrid modeling framework. Moreover, for the resulting overall infinite-dimensional hybrid system, a proper solution concept is introduced, which is necessary as many standard concepts do not apply as Zeno behavior is inevitable for the systems under study. Based on the proposed hybrid modeling framework, conditions leading to a maximally allowable transmission interval (MATI) for all of the individual communication networks are derived such that uniform global asymptotic stability (UGAS) or \mathcal Lp-stability of the overall system is guaranteed. Interestingly, by exploiting the interconnection structure, the conditions guaranteeing UGAS or \mathcal Lp-stability can be stated locally in the sense that they only involve the (local) dynamics of one subsystem in the interconnection and local conditions on the scheduling protocol. Finally, it is shown that in the linear case the derived conditions can even be stated in terms of “local” LMIs, making them amenable for computational verification. [ABSTRACT FROM AUTHOR]

This paper studies scalar integral inequalities in one-dimensional bounded domains with polynomial integrands. We propose conditions to verify the integral inequalities in terms of differential matrix inequalities. These conditions allow for the verification of the inequalities in subspaces defined by boundary values of the dependent variables. The results are applied to solve integral inequalities arising from the Lyapunov stability analysis of partial differential equations. Examples illustrate the results. [ABSTRACT FROM AUTHOR]

In this paper, we first establish a stability result for a class of linear switched systems involving Kronecker product. The problem is interesting in that the system matrix does not have to be Hurwitz at any time instant. This class of linear switched systems arises in the control of multi-agent systems under switching network topology. As applications of this stability result, we give the solvability conditions for both the leaderless consensus problem and the leader-following consensus problem for general marginally stable linear multi-agent systems under switching network topology. In contrast with some existing results, our results only assume that the dynamic graph is uniformly connected. [ABSTRACT FROM AUTHOR]

This paper considers asymptotic stability and transient performance of discrete-time piecewise affine systems. We propose a procedure to construct a nested sequence of finite-state symbolic models, each of which abstracts the original piecewise affine system and leads to linear matrix inequalities for guaranteed stability and performance levels. This sequence is in the order of decreasing conservatism, and hence gives us the option to pay more computational cost and analyze a finer symbolic model within the sequence in return for less conservative results. Moreover, in the special case where this sequence is finite, an exact analysis of stability and performance is achieved via semidefinite programming. [ABSTRACT FROM PUBLISHER]

The purpose of this note is to correct some statements and numerical results in the above paper. In particular, we will show that the stability criterion in refid="ref1"/ is equivalent to that in refid="ref2"/, rather than less conservative as claimed, and the criterion in refid="ref2"/ does apply to the numerical example suggested in refid="ref1"/. [ABSTRACT FROM AUTHOR]

In this reply, we show that, in certain cases, the analysis approach given by Turner et al. does indeed give “superior” results to that given by Park. We also show, briefly, how the analysis approach given by Turner et al. can be enhanced by considering both Zames-Falb and Popov multipliers (as in the papers by Jonsson and Turner and Kerr). [ABSTRACT FROM AUTHOR]