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In this technical note, a necessary and sufficient stability criterion for switched linear systems under dwell-time constraint is proposed by employing a class of time-scheduled homogeneous polynomial Lyapunov functions with a sufficiently large degree. The key feature of this nonconservative condition lies in its convexity in the system matrices, which explicitly facilitates its further extension to uncertain systems. Then, in order to obtain numerically testable condition, a family of LMI conditions are presented with the aid of the idea of dividing the dwell-time interval into a finite number of segments. It is proved that the non-conservativeness can be maintained with a sufficiently large interval dividing parameter. In the end, the result is straightforwardly extended to the uncertain case in virtue of the convexity in the system matrices. Numerical examples are presented to illustrate our findings. [ABSTRACT FROM PUBLISHER]

This note is intended to investigate noise-to-state stability for random nonlinear systems with state-dependent switching. Under some mild and easily verified conditions, the existence of global solution to random switched systems can be proved. Based on a reasonable requirement for the random disturbance, the criteria on noise-to-state stability of random switched systems are presented by the aid of single Lyapunov function technique. The reasonability of the obtained results is illustrated by using a mechanical model in random vibration environment. [ABSTRACT FROM AUTHOR]

In this note, the fault detection filtering problem is solved for nonlinear switched stochastic system in the T-S fuzzy framework. Our attention is concentrated on the construction of a robust fault detection technique to the nonlinear switched system with Brownian motion. Based on observer-based fault detection fuzzy filter as a residual generator, the proposed fault detection is formulated as a fuzzy filtering problem. By the utilization of the average dwell time technique and the piecewise Lyapunov function technique, the fuzzy-parameter-dependent fault detection filters are designed that guarantee the resulted error system to be mean-square exponential stable with a weighted \mathcal H\infty error performance. Then, the corresponding solvability condition for the fault detection fuzzy filter is also established by the linearization procedure technique. Finally, simulation has been presented to show the effectiveness of the proposed fault detection technique. [ABSTRACT FROM AUTHOR]

This paper proposes a Lyapunov-based switching logic within the framework of adaptive mixing control (AMC), where a weighted combination of a family of candidate controllers can be inserted in the loop to regulate the output of an uncertain plant. The proposed AMC scheme employs a bank of parallel estimators, or multiple estimators, together with a switching logic that orchestrates which estimate should be evaluated by the mixer. The switching logic is driven by input/output data and uses Lyapunov-based criteria to assess the best estimate among the bank of parallel estimates. The resulting scheme guarantees convergence of the switching signal in finite time to a controller that satisfies a Lyapunov inequality implying a prescribed stability margin. The problem of convergence to the desired controller is addressed both analytically and numerically. In contrast, most classes of continuous tuning adaptive control or switching adaptive control schemes do not guarantee that after the switching stops or the adaptation is switched off the resulting closed loop linear time-invariant (LTI) system is stable, unless there is sufficient plant excitation that guarantees convergence to the desired fixed parameter controller. The proposed scheme guarantees that if the desired controller is switched on, it will never be switched off thereafter. Furthermore, simulations demonstrate that while alternative adaptation methods can converge to an LTI unstable feedback loop, the proposed scheme consistently converges to the desired controller. [ABSTRACT FROM AUTHOR]

In this paper we deal with the stabilizability property for discrete-time switched linear systems. A recent necessary and sufficient characterization of stabilizability, based on set theory, is considered as the reference for comparing the computation-oriented sufficient conditions. The classical BMI conditions based on Lyapunov-Metzler inequalities are considered and extended. Novel LMI conditions for stabilizability, derived from the geometric ones, are presented that permit to combine generality with computational affordability. For the different conditions, the geometrical interpretations are provided and the induced stabilizing switching laws are given. The relations and the implications between the stabilizability conditions are analyzed to infer and compare their conservatism and their complexity. [ABSTRACT FROM AUTHOR]

This technical note deals with the design of mode-dependent H\infty filters for a class of discrete-time switched systems with nonlinearities. In this class of systems, when the system mode changes, the filter designed for the specific subsystem also switches accordingly. The main contribution is on the use of the information of the sojourn probability—the probability of the switched system staying in each subsystem—to build new kind of switched system model when this additional information is available. Sojourn probabilities are easier to obtain than the transition probabilities commonly used in Markovian jump systems. Applying the Lyapunov functional method, the bounded real lemma (BRL) for the resulting filtering error system is obtained in Theorem 1. The filter parameters are designed in Theorem 2 by solving a set of linear matrix inequalities. Finally, two illustrative examples are given to demonstrate the effectiveness and potential of the proposed approach. [ABSTRACT FROM AUTHOR]

An alternative approach for minimum and mode-dependent dwell-time characterization for switched systems is derived. While minimum-dwell time results require the subsystems to be asymptotically stable, mode-dependent dwell-time results can consider unstable subsystems and dwell-times within a, possibly unbounded, range of values. The proposed approach is related to Lyapunov looped-functionals, a new type of functionals leading to stability conditions affine in the system matrices, unlike standard results for minimum dwell-time. These conditions are expressed as infinite-dimensional LMIs which can be solved using recent polynomial optimization techniques such as sum-of-squares. The specific structure of the conditions is finally utilized in order to derive dwell-time stability results for uncertain switched systems. Several examples illustrate the efficiency of the approach. [ABSTRACT FROM AUTHOR]

In this note, we consider switched systems and switched systems with state reset. In particular we focus on the case of partial reset, i.e., where only some state components may undergo the action of a reset. First we consider switched systems with pre-specified (partial) reset and investigate under which conditions such systems are stable. In a second stage we consider the problem of stabilization by (partial) reset, which consists in finding a suitable (partial) reset for a given switched system that makes this system stable under arbitrary switching. [ABSTRACT FROM AUTHOR]

The standard approach to the problem of controlling linear systems with large parameter uncertainty is to seek a controller that stabilizes the system and achieves a required performance over the whole polytope of uncertainty. In the case where the latter polytope is large, the design may become very conservative. We present an alternative approach where the uncertainty polytope is divided into overlapping smaller regions and where each of these regions is assigned to a separate subsystem. Assuming that there is online information on which of the regions the parameters of the system move to, a recently developed method for H\infty design of switched system with dwell time is applied. A Lyapunov Function (LF) in a quadratic form, which is non-increasing at the switching instants, is assigned to each subsystem. This function is used to determine the stability and to find a bound on the \cal L2 -gain of the switched system. The obtained results are used to solve the corresponding robust H\infty state-feedback and static output-feedback control problems. [ABSTRACT FROM AUTHOR]

This technical note presents a new method for stability analysis and stabilization of sampled-data systems with control packet loss. It is assumed that if the control packet from the controller to the actuator is lost, then the actuator input to the plant is set to zero. The new method is based on a novel construction of piecewise differentiable Lyapunov functionals by using an impulsive system representation of sampled-data systems. A significant feature of the new Lyapunov functionals is that they are continuous at impulse times but not necessarily positive definite inside the impulse intervals. Applying the new Lyapunov functionals to sampled-data systems with control packet loss, improved criteria for stability and stabilization are derived. The new criteria are proved theoretically to be less conservative than the existing results. Illustrative examples are given which substantiate the usefulness of the proposed method. [ABSTRACT FROM AUTHOR]

Sufficient conditions are given for the stability of linear switched systems with dwell time and with polytopic type parameter uncertainty. A Lyapunov function, in quadratic form, which is non-increasing at the switching instants is assigned to each subsystem. During the dwell time, this function varies piecewise linearly in time after switching occurs. It becomes time invariant afterwards. This function leads to asymptotic stability conditions for the nominal set of subsystems that can be readily extended to the case where these subsystems suffer from polytopic type parameter uncertainties. The method proposed is then applied to stabilization via state-feedback both for the nominal and the uncertain cases. [ABSTRACT FROM AUTHOR]

This paper first investigates the stability and ℓ2-gain problems for a class of discrete-time switched systems with average dwell time (ADT) switching by allowing the Lyapunov-like functions to increase during the running time of subsystems. The obtained results then facilitate the studies on the issue of asynchronous control, where "asynchronous" means the switching of the controllers has a lag to the switching of system modes. In light of the proposed Lyapunov-like functions, the desired mode-dependent controllers can be designed since the unmatched controllers are allowed to perform in the interval of asynchronous switching before the matched ones are applied. The problem of asynchronous H∞, control for the underlying systems in linear cases is then formulated. The conditions of the existence of admissible asynchronous H∞, controllers are derived, and a numerical example is provided to show the potential of the developed results. [ABSTRACT FROM AUTHOR]

Real systems are often driven by switching reference signals which affect dynamics and/or equilibrium points. This technical note addresses the computation of upper bounds of the minimum commutation time ensuring stability for switching nonlinear systems. Specifically, we consider the cases of constant and variable equilibrium point of interest, for polynomial systems and for a class of non-polynomial systems. We hence propose upper bounds of the sought minimum commutation time by adopting homogeneous polynomial Lyapunov functions for the former case and polynomial Lyapunov functions for the latter one, which can be computed via linear matrix inequaltiy optimizations for given Lyapunov functions. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper investigates the switching stabilizability problem for a class of continuous-time switched linear systems with time-variant parametric uncertainties. First, a necessary and sufficient condition for the asymptotic stabilizability of such uncertain switched linear system is derived, under the assumption that the closed-loop switched system does not generate sliding motions. Then, an additional condition is introduced to exclude the possibility of unstable sliding motions. Finally, a necessary and sufficient for the asymptotic stabilizability of such continuous-time uncertain switched linear systems is presented. This result improves upon conditions found in the literature which are either sufficient only or necessary only. [ABSTRACT FROM AUTHOR]

Multiple Lyapunov functions are used to establish sufficient conditions for locating the limit sets of switching diffusions. The conditions lead to a number of useful results on stochastic asymptotic stability and boundedness for this class of stochastic hybrid systems. [ABSTRACT FROM AUTHOR]

In this note, a new class of hybrid impulsive and switching models is introduced and their asymptotic stability properties are investigated. Using switched Lyapunov functions, some new general criteria for exponential stability and asymptotic stability with arbitrary and conditioned impulsive switching are established. In addition, a new hybrid impulsive and switching control strategy for nonlinear systems is developed. A typical example, the unified chaotic system, is given to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]