L2-gain analysis of regenerative switched linear systems with sampled-data state-feedback control

Design of a sampled-data state feedback controller for stabilizing a nonlinear continuous-time plant is studied. The sampled-data state feedback controller is designed based on an approximate discrete-time model of the plant and it is able to exponentially stabilize the approximate discrete-time model. When the sampled-data controller applies to the continuous-time plant, the closed loop system is a hybrid system. This paper gives a sufficient condition under which the sampled-data controller exponentially stabilizes the hybrid system consisting of the continuous-time plant and the sampled-data controller.

Robust guaranteed cost control of uncertain fuzzy systems under time-varying sampling

In this paper, we investigate the sampled-data state feedback control (SDSFC) for the synchronization of Boolean control networks (BCNs) under the configuration of drive-response coupling. Necessary and sufficient conditions for the complete synchronization of BCNs are obtained by the algebraic representations of logical dynamics. Based on the analysis of the sampling periods, we establish an algorithm to guarantee the synchronization of drive-response coupled BCNs by SDSFC. An example is given to illustrate the significance of the obtained results.

Stability analysis and stabilization of LPV systems with jumps and (piecewise) differentiable parameters using continuous and sampled-data controllers

This paper provides a design of event-triggered feedback stabilisation scheme for a class of sampled-data singular systems, in which the input matrix corresponding to the algebraic equation is not full column rank. First, unlike the conventional piecewise-constant sampled-data feedback controller, a novel hybrid impulsive and sampled-data state feedback controller is designed, which can effectively match with the algebraic equation at sampling instants. An improved discrete event-triggering mechanism with checking period is proposed to achieve exponential stabilisation. Based on these, by applying the input delay approach and defining a new input-delay dependent Lyapunov functional, a sufficient stability condition is presented which ensures that the solution of the event-triggered control system exists and is unique, and the system is exponentially stable with definite decay rate. The estimate of decay coefficient is also given explicitly. Then, an optimisation-based method is developed to jointly design the hybrid controller gains and the event parameters. Finally, two simulation examples including a linearised 2-generator and 6-bus power network system are given to illustrate the validity of the new approach.

This article investigates the set stabilization of impulsive Boolean control networks (IBCNs) by sampled-data state feedback control based on a hybrid index model. It is worth mentioning that the 2-D index model has the ability to characterize the instantaneousness of ideal impulses and describe complicated impulsive behaviors. To avoid Zeno phenomenon, the judging conditions for forward completeness are derived. Subsequently, an algorithm is designed to obtain the largest sampled point control invariant set (SPCIS) of a given set in the hybrid domain, and its validity is further authenticated. Accordingly, a necessary and sufficient condition is derived for the set stabilization of IBCNs in the hybrid domain, and all time-optimal sampled-data state feedback controllers are designed. The similar results are also obtained for IBCNs in the time domain. Compared with set stabilization in the time domain, set stabilization in the hybrid domain not only focuses on the dynamics at each time instant but also concerns every jumping state. It results in that every SPCIS in the hybrid domain is a subset of a certain SPCIS in the time domain. Eventually, the λ switch with impulsive disturbances is modeled as a reduced IBCN, which is presented to demonstrate the obtained results.

Optimal [formula omitted] state feedback sampled-data control design of Markov Jump Linear Systems

For a class of inherently nonlinear systems with uncertain parameters, the global stabilization problem via sampled-data control is investigated in this paper. First of all,based on the technique of adding a power integrator and a recursive argument, a class of sampled-data state feedback controllers are proposed. Then under the proposed controller, by using a suitable Lyapunov functional, it is shown that there is a maximum allowable sampling period which can guarantee the global asymptotical stability of the closed-loop system. Since the proposed controller is discrete-time, it can be easily implemented by computers. Finally, an example is given to verify the efficiency of the proposed method.

Control design of interval type-2 fuzzy systems with actuator fault: Sampled-data control approach

Digital control of a family of time-delay feedforward systems with sparse sampling

This paper is entirely devoted to analyzing the ℋ 2 optimal state feedback sampled-data control design problem forMarkov Jump Linear Systems. Our propose is to search for a solution to this problem by imbedding it in a more general class of dynamical systems, which we call Hybrid Markov Jump Linear System (HMJLS). In this new and wide context, we show how to calculate a sampled-data state feedback control that minimizes the ℋ 2 performance index associated to the closed-loop system from the solution of a specific two-point boundary value problem. This result is adapted to provide optimal control conditions based on linear matrix inequalities (LMIs). The theory is illustrated by means of an academical example.

In this technical note, we are concerned with linear matrix inequality (LMI) approaches for solving sampled-data state-feedback control design problems of linear time-invariant systems. This short contribution discusses a simple alternative to a family of LMI approaches based on the polytopic linear difference inclusion representation of the original problem. With the aid of the so-called matrix-dilation technique, the proposed condition is capable of being directly derived from the discrete-time Lyapunov inequality without the polytopic modeling. Finally, numerical experiments are given to illustrate the results.

In this paper we study the stability and L 2 -gain properties of a class of hybrid systems that exhibit linear flow dynamics, periodic time-triggered jumps and arbitrary nonlinear jump maps. This class of hybrid systems is relevant for a broad range of applications including periodic event-triggered control, sampled-data reset control, sampled-data saturated control, and certain networked control systems with scheduling protocols. For this class of continuous-time hybrid systems we provide new stability and L 2 -gain analysis methods. Inspired by ideas from lifting we show that the stability and the contractivity in L 2 -sense (meaning that the L 2 -gain is smaller than 1) of the continuous-time hybrid system is equivalent to the stability and the contractivity in L 2 -sense (meaning that the l 2 -gain is smaller than 1) of an appropriate discrete-time nonlinear system. These new characterizations generalize earlier (more conservative) conditions provided in the literature. We show via a reset control example and an event-triggered control application, for which stability and contractivity in L 2 -sense is the same as stability and contractivity in l 2 -sense of a discrete-time piecewise linear system, that the new conditions are significantly less conservative than the existing ones in the literature. Moreover, we show that the existing conditions can be reinterpreted as a conservative l 2 -gain analysis of a discretetime piecewise linear system based on common quadratic storage/Lyapunov functions. These new insights are obtained by the adopted lifting-based perspective on this problem, which leads to computable L 2 -gain (and thus L 2 -gain) conditions, despite the fact that the linearity assumption, which is usually needed in the lifting literature, is not satisfied.

The authors relate the H/sub /spl infin// and H/sub 2/ norms for a type of MIMO hybrid system, which includes sampled-data feedback control systems, where a continuous-time plant is controlled by a digital compensator with hold and sampler. First, the authors derive the H/sub /spl infin// norm bounds for MIMO purely continuous and discrete-time systems given information concerning the location of the poles. The results are the same as those for the SISO case. Second, the authors describe upper bounds on both H/sub 2/ and H/sub /spl infin// norms for hybrid systems, based on fundamental relations derived by two different approaches, namely the hybrid state space approach and the fast sampling and lifting approach. The authors also show the properties and interpretation of a residual appearing in the bounds and investigate the upper bound of the H/sub 2/ norm for a purely continuous-time system based on the result for the general hybrid case. >

This paper investigates the sampled-data stabilization problem for a Takagi–Sugeno (T-S) fuzzy system with time delay. By taking the information of states within the intervals from $t_{k}$ to $t$ and $t$ to $t_{k+1}$ into account, a new two-side delay-dependent looped-functional is introduced which can not only relax the monotonic constraint of Lyapunov–Krasovskii functional (LKF), but also make better use of the actual sampling pattern. Furthermore the sampled-data fuzzy controller is designed to contain both the present and delayed state information, thereby enhancing the control performance and design flexibility. Based on the novel augmented LKF and improved bounding technique, less conservative stability criteria are derived in the form of linear matrix inequalities. The superiority of proposed results is shown by two simulation examples.