Necessary and sufficient conditions for the positivity and reachability of fractional descriptor continuous-time linear systems are established. The minimum energy control problem for the fractional positive descriptor systems is formulated and solved. Procedure for computation of the optimal inputs and minim value of the performance index is proposed and illustrated by a numerical example.

This study is concerned with the event-triggered control for networked control systems via dynamic output feedback controllers (DOFCs). The output measurement signals of the physical plant are sampled periodically. An output-based discrete event-triggering mechanism is introduced to choose those only necessary sampled-data packets to be transmitted through a communication network for controller design. Under this event-triggering mechanism, the resultant closed-loop system is first modelled as a linear system with an interval time-varying delay. Then a novel stability criterion is established by employing the Lyapunov–Krasovskii functional approach. Based on this stability criterion, a new sufficient condition is derived to co-design both the desired DOFCs and the event-triggering parameters. Finally, a satellite control system is taken to show the effectiveness of the proposed method.

Despite the remarkable theoretical accomplishments and successful applications of adaptive control, this field is not mature enough to solve challenging problems where strict performance and robustness guarantees are required. The needs of an approach that explicitly accounts for robust performance and stability specifications is a critical to the design of practical adaptive control systems. Towards this goal, this study extends the robust adaptive controller using multiple models, switching and tuning to multiple input multiple output and non-linear systems. The use of ‘extended superstability’, instead of superstability, allows us to establish overall performance guarantees and reduce the conservativeness of the resulting closed-loop system. The authors show that under the proposed framework, the output and states remain bounded for bounded disturbances, as a direct consequence of the passivation properties of superstability. The effectiveness of the proposed algorithm is demonstrated in numerical simulations of a non-linear continuous stirred tank reactor.

The tuning of the parameters of two types of event-based proportional–integral (PI) controllers based on symmetric send-on-delta (deadband) sampling is investigated in this study. In particular, well-known tuning rules devised for standard (continuous-time) PI controllers are compared with tuning rules properly devised for these event-based controllers in order to minimise the step response settling time. Simulations and experiments show that a satisfactory performance, namely, a performance similar to the corresponding time-driven controller, is achieved by all the tuning rules considered because of the structure of the event-based PI controller, thus making it very suitable for its use in the industry.

This study addresses the stabilisation problem of a class of discrete-time Markov jump linear systems subject to time delays which occur in both the system state and mode detection. The mode detection delay means that there exists a lag between the switching of the system modes and the switching of the corresponding controllers. The state delays are considered to be random but with upper and lower bounds, and the mode detection delay is assumed to be constant. With an extended state space, the underlying system can be remodelled as a Markov jump linear system in which the system complexity and the number of system modes are both increased to a certain extent, but remain unchanged when the mode detection delay becomes larger. A sufficient condition guaranteeing the stochastic stability of the system is obtained via a modified stochastic Lyapunov function. The effectiveness of the proposed design approach is demonstrated by a numerical example.

An adaptive loop transfer recovery (LTR) approach for uncertain systems using the Kalman filter-based disturbance accommodating control scheme is presented. This study shows that the full LTR property of disturbance accommodating control is invariant to system uncertainties and external disturbances acting on the system. Also presented here is an adaptive LTR scheme, where the system process noise intensity matrix is updated online to achieve full LTR. Numerical simulations are presented to verify the superiority of the approach compared to the traditional linear quadratic regulator/LTR.

This study considers the distributed containment control problem of second-order multi-agent systems with inherent non-linear dynamics. Two distributed control protocols with, respectively, static and adaptive control gains are proposed to ensure that the states of the followers asymptotically converge to the convex hull spanned by the corresponding states of the leaders. For the static control protocol, undirected and directed interaction topologies among the followers are taken into consideration, under which sufficient conditions on the control gains are obtained by using a Lyapunov-based approach. For the adaptive control protocol, it is proved that the containment control problem can be solved without requiring any global information if the interaction topology among the followers is undirected. Numerical examples are provided to demonstrate the effectiveness of our theoretical results.

This study presents a sum-of-squares (SOS) approach to stable control and guaranteed cost control of discrete polynomial fuzzy systems. The SOS framework presented in this paper offers a new paradigm over the existing linear matrix inequality (LMI) approaches to discrete Takagi–Sugeno (T–S) fuzzy models. At first, this study, newly introduces a discrete polynomial fuzzy model that is more general and effective than the well-known discrete T–S fuzzy model. With considering the operating domain, stable control design conditions are then derived based on state-dependent Lyapunov functions that contain quadratic Lyapunov functions as a special case. Hence, the design approach discussed in this study could be more general than the LMI design approaches based on quadratic Lyapunov functions. Moreover, this study also discusses a guaranteed cost control design which is carried out by minimising the upper bound of a given performance function. All the design conditions derived in this study can be represented in terms of SOS and are symbolically and numerically solved via the SOSOPT and the SeDuMi, respectively. Finally, the ball-and-beam system is provided as an example to illustrate the utility of the proposed SOS-based design approach.