D-stability and disturbance attenuation properties fornetworked control systems： switched system approach

Both D-stability and finite L2-gain properties are studiedfor a class of uncertain discrete-time systems with timevaryingnetwork-induced delays. By using coordinate transformand delay partition, the D-stability and H∞ performance problemsfor such networked control systems （NCSs） are equivalentlytransferred into the corresponding problems for switching systemswith arbitrary switching. Then, a sufficient condition for the existenceof the robust D-stabilizing controllers is derived in termsof linear matrix inequality （LMI）, and the design method is alsopresented for the state feedback controllers which guarantee thatall the closed-loop poles remain inside the specified disk D（α,r）and the desired disturbance attenuation level. Finally, an illustrativeexample is given to demonstrate the effectiveness of the proposedresults.

Conditions for Robust D-Stability of Discrete-Delay Perturbed Singular Systems

In this paper, a sufficient condition of robust D-stability for discrete-delay perturbed singular systems is presented, and the robust stability sufficient condition is independent of the delay. Two classes of perturbations for systems are discussed: (1) highly structured parametric perturbations; (2) unstructured parametric perturbations. An useful technique for robust pole-assignment in a specified circular region is also proposed, the criterion is tested easily, and convenient for the application in the engineering. Two examples have been given to validate the proposed method.

A Robust D-Stability of Polynomials with Nonlinearly Dependent Perturbations

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Robust D-Stability Test of LTI General Fractional Order Control Systems

This work deals with the robust D-stability test of linear time-invariant(LTI) general fractional order control systems in a closed loop where the system and/or the controller may be of fractional order. The concept of general implies that the characteristic equation of the LTI closed loop control system may be of both commensurate and non-commensurate orders, both the coefficients and the orders of the characteristic equation may be nonlinear functions of uncertain parameters, and the coefficients may be complex numbers. Some new specific areas for the roots of the characteristic equation are found so that they reduce the computational burden of testing the robust D-stability. Based on the value set of the characteristic equation, a necessary and sufficient condition for testing the robust D-stability of these systems is derived. Moreover, in the case that the coefficients are linear functions of the uncertain parameters and the orders do not have any uncertainties, the condition is adjusted for further computational burden reduction. Various numerical examples are given to illustrate the merits of the achieved theorems.

FREQUENCY DOMAIN CRITERIA FOR ROBUST D-STABILITY OF MIMO SYSTEMS BASED ON LMI METHOD

The problem of checking robust D-stability of multi-in and multi-out （MIMO） systems was studied. Three system models were introduced, i.e. multilinear polynomial matrix, polytopic polynomial matrix and feedback system model. Furthermore, the convex property of each model with respect to the parametric uncertainties was estabilished respectively. Based on this, sufficient conditions for D-stability were expressed in terms of linear matrix inequalities （LMIs） involving only the convex vertices. Therefore, the robust D-stability was tested by solving an LMI optimal problem.

Robust D-stability LMI conditions of matrix polytopes via affine parameter-dependent Lyapunov functions

The problem of the robust D-stability analysis for linear systems with parametric uncertainties is addressed. For matrix polytopes, new conditions via the affine parameter-dependent Lyapunov function of uncertain systems are developed with the benefit of the scalar multi-convex function. To be convenient for applications, such conditions are simplified into new linear matrix inequality （LMI） conditions, which can be solved by the powerful LMI toolbox. Numerical examples are provided to indicate that this new approach is less conservative than previous results for Hurwitz stability, Schur stability and D-stability of uncertain systems under certain circumstances.

State-feedback H_2/H-infinity controller design with D-stability constraints for stochastic systems

This paper addresses the state-feedback H2/H-infinity controller design that satisfies D-stability constraints for stochastic systems. Firstly, the concept of regional stability for stochastic systems is defined in linear matrix inequality（LMI） regions; Secondly, the characterization about stochastic D-stability is presented. This paper introduces a new technique to solve the regional stability problem for stochastic systems, which is different from the pole placement technique ever used in deterministic systems. Based on this, in the state-feedback case, mixed H2/H-infinity synthesis with D-stability constraints is discussed via LMI optimization.

Stability Design for the Homogeneous Platoon with Communication Time Delay

A hierarchical control framework is applied for the distributed cooperative vehicular platoon using vehicular ad-hoc networks.The parameter-space-approach-based cooperative adaptive cruise control(CACC)controller is proposed to guarantee the D-stability and the string stability considering the influence of the communication time delay and time lag of vehicular dynamic performance.This CACC controller combines the feedforward loop of the acceleration of the preceding vehicle with the feedback loop of the following errors,in which the gain of the feedforward loop is designed to decrease matching errors and the gains of the feedback loop are selected from the feasible region in the parameter space.To verify the effectiveness of the CACC controller,a six-vehicle platoon with a simplified vehicular dynamic is simulated under speed-up and stop scenarios.The simulation results demonstrate that the disturbance is attenuated along with the platoon and the following errors are convergent with well-designed convergent performance.A CarSim/Simulink co-simulation is designed to further verify the effectiveness of the hierarchical control framework and the rationality of the CACC controller in the real vehicular platoon application.The simulation results under the highway fuel economy test drive cycle show that the CACC controller improves the drive comfort and significantly decreases the following errors.

Boundary Theorem and Edge Theorem of Complex Polynomial Families

The value mapping, boundary theorem and parameterization as a new idea has afforded approaches and theory for the robust stability analysis of real polynomial families. In this note the problems of robust stability analysis of complex polynomial families, which is of significance in several engineering applications, are discussed via the above approaches. It will be shown that value mapping, boundary theorem and edge theorem can be successfully applied to the robust stability analysis of complex polynomial families.

Boundary Theorems for the Robust Stability of Complex Polynomial Families

Following our previous works, in this paper we give the general form of boundary theorems of polynomial families, with which the existing theorems for the robust stability of polynomial families can be simply and clearly proved, thus offering an effective method for further study. And some results in [2] are improved.

D-SThBILITY TESTING FOR THE INTERVALMATRIX FAMILY

This paper is concerned with the problem of D-stability testing for the interval matrix family. First, a nonlinearly or affine multilinearly parametrized interval polynomial family is considered. If the mapping from the parameter space to the coefficient space can be expressed as an affine linear mapping of at least two variables, then it is shown that the D-stability of the family is equivalent to that of its low dimensional boundaries. In light of this result, it is proved that to determine the D-stability of an interval matrix family,it suffices to check its n!2n(n-1) n-dimensional exposed faces. Finally the results obtained are extended to the case where the rows or the columns of the matrix family are perturbed independently in different polytopes, and a result analogous to that in the interval case is obtained.