Delay-dependent dissipative control for linear time-delay systems

This paper deals with the problem of delay-dependent dissipative control for a class of linear time-delay systems. We develop the design methods of dissipative static state feedback and dynamic output feedback controllers such that the closed-loop system is quadratically stable and strictly (Q,S,R)-dissipative. Sufficient conditions for the existence of the quadratic dissipative controllers are obtained by using linear matrix inequality (LMI) approach. Furthermore, a procedure of constructing such controllers from the solutions of LMIs is given. It is shown that the solvability of a dissipative controller design problem is implied by the feasibility of LMIs. The main results of this paper unify the existing results on H^∞ control and passive control.     

Output feedback robust H∞ control for spacecraft rendezvous system subject to input saturation: A gain scheduled approach

In this paper, the problem of output feedback robust H_∞ control for spacecraft rendezvous system with parameter uncertainties, disturbances and input saturation is investigated. Firstly, a full-order state observer is designed to reconstruct the full state information, whose gain matrix can be obtained by solving the linear matrix inequality (LMI). Subsequently, by combining the parametric Riccati equation approach and gain scheduled technique, an observer-based robust output feedback gain scheduled control scheme is proposed, which can make full use of the limited control capacity and improve the control performance by scheduling the control gain parameter increasingly. Rigorous stability analyses are shown that the designed discrete gain scheduled controller has faster convergence performance and better robustness than static gain controller. Finally, the performance and advantage of the proposed gain scheduled control scheme are demonstrated by numerical simulation.     

Local exponential stabilization via boundary feedback controllers for a class of unstable semi-linear parabolic distributed parameter processes

This paper addresses the problem of local exponential stabilization via boundary feedback controllers for a class of nonlinear distributed parameter processes described by a scalar semi-linear parabolic partial differential equation (PDE). Both the domain-averaged measurement form and the boundary measurement form are considered. For the boundary measurement form, the collocated boundary measurement case and the non-collocated boundary measurement case are studied, respectively. For both domain-averaged measurement case and collocated boundary measurement case, a static output feedback controller is constructed. An observer-based output feedback controller is constructed for the non-collocated boundary measurement case. It is shown by the contraction semigroup theory and the Lyapunov’s direct method that the resulting closed-loop system has a unique classical solution and is locally exponentially stable under sufficient conditions given in term of linear matrix inequalities (LMIs). The estimation of domain of attraction is also discussed for the resulting closed-loop system in this paper. Finally, the effectiveness of the proposed control methods is illustrated by a numerical example.     

Robust gain-scheduled output feedback yaw stability control for in-wheel-motor-driven electric vehicles with external yaw-moment

This paper presents a robust gain-scheduled output feedback yaw stability H_∞ controller design to improve vehicle yaw stability and handling performance for in-wheel-motor-driven electric vehicles. The main control objective is to track the desired yaw references by managing the external yaw moment. Since vehicle lateral states are difficult to obtain, the state feedback controller normally requires vehicle full-state feedback is a critical challenge for vehicle lateral dynamics control. To deal with the challenge, the robust gain-scheduled output feedback controller design only uses measurements from standard sensors in modern cars as feedback signals. Meanwhile, parameter uncertainties in vehicle lateral dynamics such as tire cornering stiffness and vehicle inertial parameters are considered and handled via the norm-bounded uncertainty, and linear parameter-varying polytope vehicle model with finite vertices is established through reducing conservative. The resulting robust gain-scheduled output feedback yaw stability controller is finally designed, and solved in term of a set of linear matrix inequalities. Simulations for single lane and double lane change maneuvers are implemented to verify the effectiveness of developed approach with a high-fidelity, CarSim^®, full-vehicle model. It is confirmed from the results that the proposed controller can effectively preserve vehicle yaw stability and lateral handling performance.     

Linear stochastic system identification using correlation techniques

The identification of linear, discrete time, scalar output systems which are driven exclusively by white, zero mean, inaccessible noise sequences is discussed. Two principal results are presented. First, two methods (least squares and an autocorrelation technique) for identifying the system characteristic equation coefficients are compared. The least squares approach is shown to be biased except for special cases. In general, the bias cannot be removed. If the state transition matrix is of the phase variable form, bias removal requires a knowledge of the measurement noise variance and all but one of the state driving noise variances. The autocorrelation technique is not biased asymptotically and does not require a knowledge of the noise variances.Secondly, it is shown that the m² elements of the state transition matrix cannot be identified uniquely from the scalar output sequence autocorrelation coefficients if the system order is higher than one. The implication of this uncertainty in the state transition matrix on optimal filtering of the output sequence is briefly discussed.     

Input–output finite-time stabilization for MJSs with time-varying delay: An observer-based approach

This paper deals with the input–output finite-time stabilization problem for Markovian jump systems (MJSs) with incompletely known transition rates. An observer-based output feedback controller is constructed to study the input–output finite-time stability (IO-FTS) problem. By using the mode-dependent Lyapunov–krasovskii functional method, a sufficient criterion checking the IO-FTS problem is provided. Then, an observer and a corresponding state feedback controller for the individual subsystem are respectively designed to solve the input–output finite-time stabilization problem for the systems. Finally, a numerical example on the mass-spring system model is investigated to bring out the advantages of the control scheme proposed in this paper.     

On the dynamics of a quantum coherent feedback network of cavity-mediated double quantum dot qubits

The purpose of this paper is to present a comprehensive study of a coherent feedback network where the main component consists of two distant double quantum dot (DQD) qubits which are directly coupled to a cavity. This main component has recently been physically realized (van Woerkom et al., Microwave photon-mediated interactions between semiconductor qubits, Physical Review X, 8(4):041018, 2018). The feedback loop is closed by cascading this main component with a beamsplitter. The dynamics of this coherent feedback network is studied from three perspectives. First, an analytic form of the output single-photon state of the network driven by a single-photon state is derived. In contrast to the experimental observations made in the above paper where a laser is used as input, new interesting physical phenomena are revealed by means of single-photon input. Second, excitation probabilities of DQD qubits are computed when the network is driven by a single-photon input state. Finally, if the input is vacuum but one of the two DQD qubits is initialized in its excited state, the explicit expression of the steady-state joint system-field state is derived, which shows that the output single-photon field and the two DQD qubits can form an entangled state if the transition frequencies of two DQD qubits are equal. This analytical expression can be used to interpret experimental results in the existing literature.     

Global practical tracking for nonlinear systems with uncertain dead-zone input via output feedback

In this paper, global practical tracking is investigated via output feedback for a class of uncertain nonlinear systems subject to unknown dead-zone input. The nonlinear systems under consideration allow more general growth restriction, where the growth rate includes unknown constant and output polynomial function. Without the precise priori knowledge of dead-zone characteristic, an input-driven observer is designed by introducing a novel dynamic gain. Based on non-separation principle, a universal adaptive output feedback controller is proposed by combining dynamic high-gain scaling approach with backstepping method. The controller proposed guarantees that the closed-loop output can track any smooth and bounded reference signal by any small pre-given tracking error, while all closed-loop signals are globally bounded. Finally, simulation examples are given to illustrate the effectiveness of our dynamic output feedback control scheme.     

Global output feedback stabilization for a class of nonlinear systems with multiple uncertainties

This paper investigates the problem of global output feedback stabilization for a class of nonlinear systems with multiple uncertainties. A remarkable feature lies in that the system to be considered is not only involved dynamic and parametric uncertainties but also the measurement output affected by an uncertain continuous function, which leads to the obstacles in the constructions of a state observer and a controller. By revamping the double-domination approach with the skillful implantation of a dynamic gain scheme and nonnegative integral functions, a new design strategy is established by which a global output feedback stabilizer together with a novel state observer can be constructed successfully. The novelty of the presented design is attributed to a perspective in dealing with the output feedback stabilization undergone the unknown continuous (time-varying) output function and dynamic/parametric uncertainties. Finally, an illustrative example is provided to illustrate the effectiveness of the theoretical results.     

Boundary stabilization of a class of reaction–advection–diffusion systems via a gradient-based optimization approach

In this paper, the boundary stabilization problem of a class of unstable reaction–advection–diffusion (RAD) systems described by a scalar parabolic partial differential equation (PDE) is considered. Different the previous research, we present a new gradient-based optimization framework for designing the optimal feedback kernel for stabilizing the unstable PDE system. Our new method does not require solving non-standard Riccati-type or Klein–Gorden-type PDEs. Instead, the feedback kernel is parameterized as a second-order polynomial whose coefficients are decision variables to be tuned via gradient-based dynamic optimization, where the gradients of the system cost functional (which penalizes both kernel and output magnitude) with respect to the decision parameters are computed by solving a so-called “costate” PDE in standard form. Special constraints are imposed on the kernel coefficients to ensure that the optimized kernel yields closed-loop stability. Finally, three numerical examples are illustrated to verify the effectiveness of the proposed approach.     

Delay-dependent guaranteed cost control for uncertain 2-D discrete systems with state delay in the FM second model

This paper is concerned with the problem of delay-dependent guaranteed cost control for uncertain two-dimensional (2-D) state delay systems described by the Fornasini and Marchesini (FM) second state-space model. Given a scalar α∈(0,1), a sufficient condition for the existence of delay-dependent guaranteed cost controllers is given in terms of a linear matrix inequality (LMI) based on a summation inequality for 2-D discrete systems. A convex optimization problem is proposed to design a state feedback controller stabilizing the 2-D state delay system as well as achieving the least guaranteed cost for the resulting closed-loop system. Finally, the simulation example of thermal processes is given to illustrate the effectiveness of the proposed result.     

LQ preview state feedback with output regulation constraint

This paper addresses the output regulation problem for a class of preview control systems, and derives a state feedback law which suppresses the steady-state error caused by the excitation from polynomial or sinusoidal exogenous inputs. Recently, the output regulation condition for the broader class of distributed parameter systems is characterized via the operator regulator equation. We show that a solution of the operator regulator equation specialized to the preview control system is obtained by solving the matrix regulator equation, and provide the state feedback law which attenuates the transient error optimally with respect to an LQ (Linear Quadratic) performance index.     

Input–output decoupling control design for switched Boolean control networks

We investigate the input–output decoupling problem of switched Boolean control networks (SBCNs) in this paper. Based on the matrix expression of Boolean functions, the dynamics of SBCNs are converted into an algebraic form via semi-tensor product of matrices first. Then, using the redundant variable separation technique, we give the necessary and sufficient conditions for the existence of three kinds of controllers to detect whether an SBCN can be input–output decomposed or not, respectively, including the open-loop controllers, the state feedback controllers, and the output feedback controllers. Meanwhile, a constructive procedure is presented to construct the open-loop controllers, as well as the state feedback controllers and output feedback controllers. Finally, an illustrative example is given to show that the new results obtained are effective.     

Sufficient and necessary conditions for stabilizing singular fractional order systems with partially measurable state

This paper is concerned with the stabilization problem of singular fractional order systems with order α?∈?(0, 2). In addition to the sufficient and necessary condition for observer based control, a sufficient and necessary condition for output feedback control is proposed by adopting matrix variable decoupling technique. The developed results are more general and efficient than the existing works, especially for the output feedback case. Finally, two illustrative examples are given to verify the effectiveness and potential of the proposed approaches.     

The feedback interconnection of lumped linear time-invariant systems

This paper considers the feedback interconnection of two multi-input multi-output subsystems characterized by rational transfer functions ₁ and functions are not assumed to be proper nor exponentially stableThe effect of output disturbances on stability is taken into account. Ten examples are given to show that instabilities may appear anywhere around the loop. Next, under a sequence of successively more restrictive assumptions, we prove four sets of necessary and sufficient conditions for the exponential stability of the system. Using coprime factorizations, we obtain four equivalent expressions for the system characteristic polynomial. Two stability tests are derived, the first one is based exclusively on transfer functions, the second is based on the characteristic polynomial. The paper ends by providing translation rules for reformulating all definitions and theorems for the discrete-time case (i.e. instead of Laplace transforms use Z-transforms, etc.).     

An overview of the applications and solutions of a fundamental matrix equation pair

Equation TA−FT=LC (F is stable) is necessary and sufficient for the output of a feedback compensator (F,L,K_Z,K_y) to converge to a state feedback (SF) signal for a constant K, where (A,B,C,0) is the open loop system and TB is the compensator gain to the open loop system input. Thus, equation TB=0 is (1) the defining condition for this feedback compensator to be an output feedback compensator. Equation TB=0 is also the necessary and sufficient condition to (2) fully realize the critical loop transfer function and robust properties of SF control if K is systematically designed. Furthermore, because B is compatible to the open loop system gain to its unknown inputs and its input failure signals, TB=0 is also necessary for (3) unknown input observers and (4) failure detection and isolation systems. Finally, this equation pair (TA−FT=LC, TB=0) is the key condition of a really systematic and explicit design algorithm for (5) eigenstructure assignment by static output feedback control. This paper reviews the existing solutions of this equation pair, and points out that a general and exact solution is uniquely direct, simple, and decoupled. This paper also points out that these unique features also enable two decisive advantages: (1) the systematic compensator order adjustment and (2) a simple and approximate solution which is general to all systems (A,B,C,0) and which can be simply added to the exact solution whether it exists or not.     

Scattering of plane waves from an eccentrically coated metallic sphere

In this paper the scattering of plane electromagnetic waves from eccentrically coated metallic spheres is considered. Inhomogeneous, surface, singular integral equations are used to formulate the problem. Their solution is obtained in terms of spherical vector wave functions in conjunction with related addition theorems. Analytical, closed-form results are obtained in the case of small eccentricities kd, where d is the distance between the two centers and k the wave number of the dielectric coating. Thus the scattered field and the various scattering cross-sections of the problem are given by expressions of the form: S(d) = S(0)[1+g’(kd)+g”(kd)²+0(kd)³]. Numerical and graphical results for various values of the parameters are also discussed.     

The solution to matrix equation AX+XC=B

In this note, the problem of solution to the matrix equation AX+X^TC=B is considered by the Moore-Penrose generalized inverse matrix. A general solution to this equation is obtained. At the same time, some useful conclusions are made, which play important roles in the linear system theories and applications.     

具有二次性能指标的最优输出反馈的一个必要条件

本文用矩阵的秩这个工具考察了有限维线性系统具有二次性能指标的最优输出反馈问题，得到了一个必要条件。特殊情形下，这一条件可以演化为最优输出反馈增益与观测矩阵的乘积即为状态反馈增益这个相当清晰的关系。