On the factorization of rational matrices depending on a parameter

In 1961 Youla published his paper “On the factorization of rational matrices”. He proved that any proper rational para-Hermitian matrix that is positive definite on the imaginary axis can be factorized as the product of a proper rational matrix, stable with respect to the closed right half plane, and its adjoint. In this paper it is proved that for any positive definite, nonstrictly proper matrix this factorization can be given depending analytically on the original matrix, in a sufficiently small neighbourhood. This result is applied to the problem of metrizing the space of transfer matrices of linear systems, in accordance with Vidyasagar's graph topology.     

Coprimeness properties of nonlinear fractional system realizations

In this paper, the relationship between the Bezout and the set-theoretic approaches to left coprimeness is studied. It is shown that left coprimeness in the set-theoretic sense implies left coprimeness in the Bezout sense. In addition to these results, we investigate whether some properties for linear left coprime realizations carry over to the nonlinear case, for example we examine the relations between two left coprime realizations of the same system.     

Coprime factors reduction methods for linear parameter varying and uncertain systems

We present a generalization of the coprime factors model reduction method of Meyer and propose a balanced truncation reduction algorithm for a class of systems containing linear parameter varying and uncertain system models. A complete derivation of coprime factorizations for this class of systems is also given. The reduction method proposed is thus applicable to linear parameter varying and uncertain system realizations that do not satisfy the structured ℓ₂-induced stability constraint required in the standard nonfactored case. Reduction error bounds in the ℓ₂-induced norm of the factorized mapping are given.     

On strong stabilization for linear time-varying systems

This paper deals with the strong stabilization problem for linear time-varying systems and gives a sufficient condition, in terms of the coprime factors, for the existence of strong stabilizers for such a system.     

Practical stabilization of a class of uncertain nonlinear systems

In this paper the problem of robust control of a class of nonlinear systems with internal and input channel uncertainties is addressed. The proposed control algorithm reflects the two-level structure of the plant and guarantees the system uniform asymptotic stability with respect to an arbitrary neighbourhood of the nominal system stability point.     

Coprimeness properties of nonlinear fractional system realizations

In this paper, the relationship between the Bezout and the set-theoretic approaches to left coprimeness is studied. It is shown that left coprimeness in the set-theoretic sense implies left coprimeness in the Bezout sense. In addition to these results, we investigate whether some properties for linear left coprime realizations carry over to the nonlinear case, for example we examine the relations between two left coprime realizations of the same system.     

Simultaneous controller design for time-varying linear systems

In this paper, we establish the parametrization of all simultaneously stabilizing controllers for two time-varying linear systems. A new approach to the simultaneous stabilization of three time-varying linear systems is also provided.     

Control design for a class of nonlinear continuous-time systems

This paper addresses the control design problem for a certain class of continuous-time nonlinear systems subject to actuator saturations. The system under consideration consists of a system with two nested nonlinearities of different type: saturation nonlinearity and cone-bounded nonlinearity. The control law investigated for stabilization purposes depends on both the state and the cone-bounded nonlinearity. Constructive conditions based on LMIs are then provided to ensure the regional or global stability of the system. Different points, like other approaches issued from the literature, are quickly discussed. An illustrative example allows to show the interest of the approach proposed.     

Hybrid dead-beat observers for a class of nonlinear systems

This paper studies both the full order and the reduced order dead-beat observer problem for a class of nonlinear systems, linear in the unmeasured states. A novel hybrid observer design strategy is proposed, with the help of the notion of strong observability in finite time. The proposed methodology is applied for the estimation of the frequency of a sinusoidal signal. The results show that accurate estimation can be provided even if the signal is corrupted by high frequency noise. A brief discussion of the robustness properties of the proposed observer with respect to measurement errors is also provided.     

On the Lyapunov-based adaptive control redesign for a class of nonlinear sampled-data systems

Stabilization of the exact discrete-time models of a class of nonlinear sampled-data systems, with an unknown parameter, is addressed. Given a Lyapunov-based continuous-time adaptive controller that ensures some stability properties for the closed-loop system, a sufficient condition for the design of high order discrete-time controllers is given. The stability analysis is carried out considering the truncated Fliess series of the Lyapunov difference equation. Due to the appearance of power terms of the unknown parameter, the problem is reparameterized in a convex-like form and an estimation law for the new unknown parameter is derived with no need of overparametrization or projection techniques. Then, assuming appropriate conditions hold, high order controllers can be designed. The boundedness of the extended state vector is ensured under some conditions, for a sufficiently small sampling period. It is shown how increasing the controller order can improve system performance.     

Global adaptive output regulation of a class of nonlinear systems with nonlinear exosystems

This paper deals with global output regulation with nonlinear exosystems for a class of uncertain nonlinear output feedback systems. The circle criterion is exploited for the internal model design to accommodate the nonlinearities in the exosystems, and the explicit conditions are given for the exosystems such that the proposed internal model design can be applied. The uncertainties of the output feedback systems are in the form of unknown constant parameters, and adaptive control techniques are used to ensure the global stability of the proposed control design for output regulation.     

Global stabilization of a certain class of nonlinear systems

Systems are considered which can be reduced to a regular form and possess an invariant manifold such that the restriction of the system to the manifold is globally asymptotically stable (GAS). We construct a feedback which renders the manifold globally attracting. It was proved that in this situation boundedness of all orbits is necessary and sufficient for the control system to be GAS. A Lyapunov type condition for the latter property adapted to the situation in question is given. Results of Andreini, Bacciotti, and Stefani are shown to be a special case of our result.     

Terminal sliding mode observers for a class of nonlinear systems

This paper proposes a terminal sliding mode observer for a class of nonlinear systems to achieve finite time convergence for all error states. Compared to standard sliding mode observers which only enable finite time convergence of the output error, the observer in this paper makes use of fractional powers to reduce other non-output errors to zero in finite time. A 2-degree-of-freedom robotic manipulator is used to demonstrate the effectiveness of the proposed observer.     

Robustness for time-varying systems

We consider robust optimization for time-varying systems in terms of perturbations of fractional representations. Upper and lower bounds are given for the maximal radius of the operator ball around a given plant which can be stabilized by a single compensator. In the time-invariant case, these numbers are equal.     

一类非线性系统的次优控制研究

考虑一类关系度不确定且零动态稳定的非线性系统的控制器设计问题．利用预测控制概念,通过选用较为全面的二次型性能指标,对输出进行高阶泰勒级数展开,推导出一种非切换的解析次优控制律,进而得出了在该控制律下闭环系统局部稳定的充分条件．仿真例子验证了该控制算法具有较好的动态性能,与已有的近似线性化方法相比,显示了该控制策略的优越性．     

Observer-based control of a class of time-delay nonlinear systems having triangular structure

Time-delay systems constitute a special class of dynamical systems that are frequently present in many fields of engineering. It has been shown in the literature that the existence of a stabilizing observer-based controller is related to delay-dependent conditions that are generally satisfied for a small time delay. Motivating works towards reducing the conservatism of the results are among the on-going research topics especially when partial-state measurements are imposed. This paper investigates the problem of observer-based stabilization of a class of time-delay nonlinear systems written in triangular form. First, we show that a delay nonlinear observer is globally convergent under the global Lipschitz condition of the system nonlinearity. Then, it is shown that a parameterized linear feedback that uses the observer states can stabilize the system whatever the size of the delay. An illustrative example is provided to approve the theoretical results.     

Robust global stabilization of a class of uncertain feedforward nonlinear systems

The problem of global asymptotically stabilizing a certain class of uncertain feedforward nonlinear systems is considered. The control law is obtained by nesting saturation functions whose amplitude can be rendered arbitrarily small. With respect to previous works on the subject the design procedure is able to deal with uncertain (possibly time-varying) parameters ranging within the prescribed compact sets which can affect also the linear approximation of the system. The small gain theorem for nonlinear systems which are input to state stable “with restrictions” is shown to be a key tool for designing a state feedback saturated control law.     

Affine and predictive control policies for a class of nonlinear systems

The input-state linear horizon (ISLH) for a nonlinear discrete-time system is defined as the smallest number of time steps it takes the system input to appear nonlinearly in the state variable. In this paper, we employ the latter concept and show that the class of constraint admissible N-step affine state-feedback policies is equivalent to the associated class of constraint admissible disturbance-feedback policies, provided that N is less than the system’s ISLH. The result generalizes a recent result in [Goulart, P. J., Kerrigan, E. C., Maciejowski, J. M. (2006). Optimization over state feedback policies for robust control with constraints. Automatica, 42(4), 523-533] and is significant because it enables one: (i) to determine a constraint admissible state-feedback policy by employing well-known convex optimization techniques; and (ii) to guarantee robust recursive feasibility of a class of model predictive control (MPC) policies by imposing a suitable terminal constraint. In particular, we propose an input-to-state stabilizing MPC policy for a class of nonlinear systems with bounded disturbance inputs and mixed polytopic constraints on the state and the control input. At each time step, the proposed MPC policy requires the solution of a single convex quadratic programme parameterized by the current system state.     

Global stabilization for a class of switched nonlinear feedforward systems

The problem of global stabilization for a class of switched nonlinear feedforward systems under arbitrary switchings is investigated in this paper. Based on the integrator forwarding technique and the common Lyapunov function method, we design bounded state feedback controllers of individual subsystems to guarantee asymptotic stability of the closed-loop system. A common coordinate transformation of all subsystems is exploited to avoid individual coordinate transformations for subsystems that are required when applying the forwarding recursive design scheme. An example is provided to demonstrate the effectiveness of the proposed design method.     

Fault tolerant cooperative control for a class of nonlinear multi-agent systems

This paper studies the target aggregation problem for a class of nonlinear multi-agent systems with the time varying interconnection topology. The general neighboring rule-based linear cooperative protocol is developed and a sufficient aggregation condition is derived. Moreover, it is shown that in the presence of agent faults, the target point is still reached by adjusting some weights of the cooperative protocol without changing the structure of the topology. An unmanned aerial vehicle team example illustrates the efficiency of the proposed approach.