In this study, the robust stability of continuous-time switched linear systems is investigated under the assumptions that the matrices of the associated linear subsystems are subjected to affine perturbations. The notion of structured stability radius of a switched linear system which is asymptotically exponentially stable w.r.t. arbitrary switchings is introduced. Some lower bounds and upper bounds for estimating this radius are established, by using the system's common quadratic Lyapunov functions and via an approach based on solutions comparison principle. When the nominal switched system is of special structures (for instance when all matrices of subsystems are normal) the obtained bounds yield easily computable formulas for calculating or estimating the system's stability radius. Several examples are provided to illustrate the authors' approach.

This study proposes a model-free distributed output feedback control scheme that achieves synchronisation of the outputs of the heterogeneous follower agents with that of the leader agent in a directed network. A distributed two degree of freedom approach is presented that separates the learning of the optimal output feedback and the feedforward terms of the local control law for each agent. The local feedback parameters are learned using the proposed off-policy Q-learning algorithm, whereas a gradient adaptive law is presented to learn the local feedforward control parameters to achieve asymptotic tracking of each agent. This learning scheme and the resulting distributed control laws neither require access to the local internal state of the agents nor do they need an additional distributed leader state observer. The proposed approach has the advantage over the previous state augmentation approaches as it circumvents the need of introducing a discounting factor in the local performance functions. It is shown that the proposed algorithm converges to the optimal solution of the algebraic Riccati equation and the output regulator equations without explicitly solving them as long as the leader agent is reachable directly or indirectly from all the follower agents. Simulation results validate the proposed scheme.

In this study, the event-triggered distributed fault detection problem is investigated for a class of discrete-time uncertain systems in the finite frequency domain. A sensor network is utilised to collect the information of interest, and an event-triggered communication scheme is adopted to alleviate the communication burden. For the addressed problem, a distributed fault detection filter is designed based on the measurement information from its neighbouring nodes and itself by the given topology. In addition, a fashionable index, named as performance, is employed in order to simultaneously achieve the residual sensitivity to faults and the robustness against disturbances. By resorting to Euler's formula combined with Lyapunov stability theory, some sufficient conditions are established to satisfy the desired performance over a given finite-frequency domain, and the distributed fault detection filter gains are explicitly characterised by solving a series of linear matrix inequalities. A simulation example is conducted to illustrate the feasibility of the proposed filter design technique.

The containment problem of heterogeneous multi-agent systems with fixed time delay under directed network is considered for both continuous-time and discrete-time multi-agent systems. Leaders and followers have different dynamics, modelled by double-integrator and single-integrator, respectively. It is also assumed that all leaders are stationary. Unlike the current approach in the literature which utilises LMIs to derive sufficient condition for containment reaching, the authors employ Laplace transform/Z-transform and final value theorem to obtain the necessary and sufficient condition which guarantees the containment of follower agents in the presence of communication delays. This approach gives the exact maximum allowed time delay, which is larger than the bound obtained by previous approaches. This study also proposes a noble reduced-order dynamic method, by adding virtual agents, in order to use final value theorem for stability analysis in the presence of heterogeneity in the network. In the end, to illustrate the effectiveness of the theoretical results, simulation examples are provided.

In this study, the stability problem of continuous-time switched systems composed fully of unstable subsystems is considered. Unlike the hybrid conditions derived in previous literature, this study used a novel time-dependent quadratic Lyapunov function approach and a convex sufficient condition for switched linear systems is proposed in the framework of bounded maximum average dwell time (BMADT). The resulting condition in this study is enforced using the sum of squares programming. Then, the condition for switched linear systems is extended to uncertain systems and the robust stability condition is derived. Moreover, a new stability result of continuous-time switched systems with all subsystems unstable is investigated based on the BMADT conditions. The simulation shows that it is better than the results in previous literature. Two numerical examples are proposed to illustrate the authors' approach.

The present study mainly focuses on designing a stochastic sampled-data controller for chaotic Takagi–Sugeno (T–S) fuzzy systems. Distinct to the existing controller schemes, in this work, the random time delay is introduced into the proposed control scheme that ensures the exponential stabilisation of T–S fuzzy models. In addition, the input delays are assumed to be randomly time-varying, which copes with the traditional uncorrelated Bernoulli distributed sequences. Based on the proposed Lyapunov–Krasovskii functional and using new weighted integral inequalities, the stability and stabilisation conditions are derived and expressed in terms of linear matrix inequalities, which ensure the exponential stability of the states. Finally, in the simulation results, the chaotic nature of two dynamical systems are considered for validation of the derived conditions. From the simulation results, it is concluded that the proposed method can provide better stability performance and less conservative results.

This study addresses the consensus problem for linear multi-agent systems subject to external disturbances under the leaderless framework. A novel distributed dynamic output feedback control protocol is proposed, which utilises not only relative output information of neighbouring agents but also relative state information of neighbouring controllers. Through model transformation, the consensus control problem of multi-agents network is reduced to a set of independent stabilisation subproblems for n-dimensional linear systems. Sufficient analysis conditions are derived using the Lyapunov method. An important contribution of this work lies in that the leaderless output-feedback consensus synthesis conditions are convexified without introducing any conservatism and formulated as linear matrix inequalities, which can be solved efficiently via convex optimisation. This is achieved by using a novel dynamic output-feedback controller structure. A numerical example has been used to demonstrate the advantage of theoretical results.

Finite-time asynchronous control problem is discussed for positive Markovian jump systems in this study. The non-synchronous behaviours generated between the system modes and controller modes are fully considered. To ensure the closed-loop system positivity and finite-time boundedness with a guaranteed performance level, a sufficient condition on the existence of an asynchronous controller is first established by applying Lyapunov–Krasovskii functional approach and recursive matrix inequality methods. Then, with the aid of matrix conversions, the specific form of controller gain matrices can be constructed by solving linear matrix inequality (LMI) conditions. A numerical example is presented and application is illustrated to validate the proposed results by employing a pest's age-structured population dynamic model.

Discovering early signatures of voltage instability can enhance situational awareness and facilitate emergency control. Such signatures usually appear as decaying trends in load voltages and increase in reactive power output of generators. Discrete control actions such as frequent switching of load tap changer (LTC) and capacitor banks, that are otherwise unmonitored, can also be crucial indicators of a voltage problem. Hence, the authors propose a unified early warning scheme (EWS) for detecting voltage instability. To quantify and correlate spatial, temporal (spatio-temporal) trends and level changes, the authors use a multivariate, adaptive trend and level (T&L) filter. A unique feature of the proposed scheme is the signature authentication, by verifying simultaneity in T&L changes across multivariate time series. The authors show that, by extrapolating trends, limit violations in bus voltages and generator reactive power output can be estimated well in advance. Further, the level-change detection logic is shown to have the ability to detect frequent LTC-actions directly from the bus voltage time series. While the T&L filtering scheme is validated on field phasor measurement unit (PMU) datasets, EWS and emergency control is demonstrated on the classical 10-bus voltage stability test system.

In this study, the authors propose a new algorithm for the flocking problem of multi-agent systems with the dynamic virtual leader under the sampled-data frameworks. A necessary time-varying condition is derived on the sampling period for preserving connectivity of the network and avoiding collision among agents. Then, defining a new energy function, it is proved that using a connectivity-preserving potential function and under the sampling period which satisfies the necessary condition, an asymptotic flocking motion is achievable. Under the proposed sampled-data flocking algorithm, the connectivity preservation of the network and collision avoidance among agents are guaranteed as well as the velocity convergence of all agents to that of the virtual leader is ensured. Moreover, employing the upper bound of the energy function, they specify an upper bound of the sampling period which could satisfy the time-varying necessary condition. Finally, they present a numerical simulation to illustrate the theoretical results.