Huijun Gao

Fault-tolerant control of Markovian jump stochastic systems via the augmented sliding mode observer approach

This paper is concerned with the stabilization problem for a class of Markovian stochastic jump systems against sensor fault, actuator fault and input disturbances simultaneously. In the proposed approach, the original plant is first augmented into a new descriptor system, where the state vector, disturbance vector and fault vector are assembled into the state vector of the new system. Then, a novel augmented sliding mode observer is presented for the augmented system and is utilized to eliminate the effects of sensor faults and disturbances. An observer-based mode-dependent control scheme is developed to stabilize the resulting overall closed-loop jump system. A practical example is given to illustrate the effectiveness of the proposed design methodology.

Leader-following consensus of a class of stochastic delayed multi-agent systems with partial mixed impulses

In this paper, the exponential leader-following consensus problem is investigated for a class of nonlinear stochastic networked multi-agent systems with partial mixed impulses and unknown time-varying but bounded delays. The main feature of partial mixed impulses is that time-varying impulses are not only composed of synchronizing and desynchronizing impulses simultaneously but they are also injected into a fraction of nodes in multi-agent systems. Three kinds of partial mixed impulses are proposed: fixed partial mixed impulses, periodic partial mixed impulses, and try-once-discard-like partial mixed impulses. By means of the Lyapunov function theory and the comparison principle, conditions are derived for ensuring global exponential leader-following consensus under the presented three kinds of partial mixed impulses. Simulations of leader-following consensus of robotic systems are provided to validate the effectiveness of the proposed results and to show the advantages of the proposed partial mixed impulses.

Cluster synchronization in directed networks of partial-state coupled linear systems under pinning control

This paper investigates the cluster synchronization for network of linear systems via a generalized pinning control strategy which allows the network of each cluster to take relaxed topological structure. For the case with fixed topology, it is shown that a feasible feedback controller can be designed to achieve the given cluster synchronization pattern if the induced network topology of each cluster has a directed spanning tree and further compared to the couplings among different clusters, the couplings within the each cluster are sufficiently strong. An extra balanced condition is imposed on the network topology of each cluster to allow for the cluster synchronization under arbitrary switching network topologies. Such a balanced condition can be removed via the use of dwell-time technique. For all the cases, the lower bounds for such strengths of couplings within each cluster that secure the synchronization as well as cluster synchronization rate are explicitly specified. Finally, some illustrative examples are provided to demonstrate the effectiveness of the theoretical findings.

Passivity-preserving model reduction with finite frequency H ∞ approximation performance

This paper is concerned with model reduction for passive systems. For a given linear time-invariant system that is stable and positive real (PR), our goal is to find a PR reduced-order model to approximate it, and our attention is focused on reducing the error with respect to a finite frequency H ∞ performance, which is the most remarkable difference between the proposed approach and the existing ones. First, by applying multiplier expansion, new conditions in terms of linear matrix inequalities are derived for characterizing the positive realness of the reduced-order model and the finite frequency H ∞ performance of the error system. A necessary and sufficient condition is then established for parameterizing a PR reduced-order model with finite frequency H ∞ approximation performance, based on which, an iterative algorithm is constructed for numerically exploring such a reduced-order model. Particularly, a partial multiplier expansion treatment is introduced, which greatly reduces the decision variables but does not cause conservatism to the derived conditions. The proposed method is also extended to robust passivity-reserving model reduction with polytopic uncertainty. Finally, we provide two numerical examples about RLC circuits to show the effectiveness and advantages of the proposed model reduction method.

Adaptive partial-state feedback control for stochastic high-order nonlinear systems with stochastic input-to-state stable inverse dynamics

This paper aims to solve the adaptive stabilization problem for a class of stochastic high-order nonlinear systems with stochastic inverse dynamics and nonlinear parameterization. Under the weaker assumptions on stochastic inverse dynamic and nonlinear functions, by generalizing the adding a power integrator technique, using the idea of changing supply function and parameter separation technique, a smooth adaptive partial-state feedback controller is constructed to render the closed-loop system globally stable in probability and all states can be regulated to the origin almost surely. The effectiveness of the designed controller is demonstrated by a simulation example.

H∞ mode reduction for two-dimensional discrete state-delayed systems

The problem of H-infinity model reduction for two-dimensional (2-D) discrete systems with delay in state is considered. The mathematical model of 2-D systems is established on the basis of the well-known Fornasini–Marchesini local state-space. First, conditions are established to guarantee the asymptotic stability and a prescribed noise attenuation level in the sense for the underlying system. For a given stable system, attention is focused on the construction of a reduced-order model, which approximates the original system well in an norm sense. Sufficient conditions are proposed for the existence of admissible reduced-order solutions. Since these obtained conditions are not expressed as strict linear matrix inequalities (LMIs), the cone complementary linearisation method is exploited to cast them into sequential minimisation problems subject to LMI constraints, which can be readily solved using standard numerical software. These obtained results are further extended to more general cases whose system states contain multiple delays. Two numerical examples are provided to demonstrate the effectiveness of the proposed techniques.

Design of delta-sigma modulators via generalized Kalman-Yakubovich-Popov lemma

This paper is concerned with the design of delta-sigma modulators via the generalized Kalman-Yakubovich-Popov lemma. The shaped noise transfer function (NTF) is assumed to have infinite impulse response, and the optimization objective is minimizing the maximum magnitude of the NTF over the signal frequency band. By virtue of the GKYP lemma, the optimization of an NTF is converted into a minimization problem subject to quadratic matrix inequalities, and then an iterative algorithm is proposed to solve this alternative minimization problem. Each iteration of the algorithm contains linear matrix inequality constraints only and can be effectively solved by the existing numerical software packages. Moreover, specifications on the NTF zeros are also integrated in the design method. A design example demonstrates that the proposed design method has an advantage over the benchmark one in improving the signal-to-noise ratio.

An input delay approach to digital control of suspension systems

This paper investigates the problem of robust sampled-data Hinfin control for active vehicle suspension systems. By using an input delay approach, the active vehicle suspension system with sampling measurements is transformed into a continuous-time system with a delay in the state. The transformed system contains possibly non-differentiable time-varying state delay. The controller design is cast into a convex optimization problem with LMI constraints. A quarter-car model with active suspension system is considered and the effectiveness of the proposed approach is illustrated by a realistic design example.