Stabilization of minimum phase nonlinear systems by dynamic outputfeedback

In this paper, the stabilization problem of minimum phase nonlinear systems by dynamic output feedback is investigated. It is shown that if the zero dynamics of an affine nonlinear system is asymptotically stable according to the kth approximation, then the system is stabilizable by dynamic output feedback. The proof is constructive, which provides a method to design the stabilizer. The result is applied to investigating the stabilization problem of the rotating stall in axial flow compressors     

Pole assignment for linear periodic systems by memoryless outputfeedback

We consider linear periodic discrete-time systems. We are interested in the problem of placing the poles of the monodromy map by means of periodic output feedback of the same or multiple period. It is well known that, in general, the poles of time-invariant systems cannot be assigned by constant output feedback. This is in contrast with what can be obtained in the context of time-variant systems. The main contribution of this paper is that periodic output feedback suffices for pole placement of periodic systems     

Optimal stabilization of linear systems via decentralized outputfeedback

Presents an approach to the optimal stabilization of a linear time-invariant system via decentralized control. The class of controllers considered does not restrict the controller to be finite dimensional or time invariant. In fact, the controller structure proposed can be regarded as a form of time varying sampled data control. The main result of the paper presents a scheme for constructing a collection of decentralized controllers which stabilizes the system and is optimal with respect to a quadratic performance index     

Insensitive observers for discrete time linear systems

This paper considers the problem of designing an observer insensitive to system parameter variations in discrete time linear multivariable systems. A K-insensitive observer is defined as an observer that can reconstruct a linear function of the state vector in spite of the variations of system parameters, provided the initial state of the observer is suitably chosen. A deadbeat observer is defined to be an observer that reconstructs the linear function for an arbitrary initial condition of the observer. Then, the existence of the K-insensitive observer is examined, and the class of K-insensitive observers is characterized. A necessary and sufficient condition is derived under which the K-insensitive deadbeat observer can be designed, and a simple algorithm is proposed to design the observer. The resulting observer is shown to be stable. The order of the observer is evaluated. The condition for generic solvability of the problem is also given.     

Estimation in linear discrete systems with multiple time delays

The method of orthogonal projection is used to derive the equations for optimally estimating the state of a nonstationary linear discrete system with multiple time delays. A Kalman-type filter is developed, along with the necessary recursive error and cross error covariance matrix equations. A numerical example is included.     

H_∞ controller synthesis of piecewise discrete time linear systems

This paper presents an H∞ controller design method for pieccwise discrete time linear systems based on a piecewise quadratic Lyapunov function. It is shown that the resulting closed loop system is globally stable with guaranteed H∞ perfomiance and the controller can be obtained by solving a set of bilinear lnatrLx inequalities. It has been shown that piecewise quadratic Lyapunov functions are less conservative than the global qnadnmc Lyapunov functions. A simulation example is also given to illustrate the advantage of the proposed approach.     

Anisotropy-based performance analysis of linear discrete time invariant control systems

The anisotropic norm of a linear discrete-time-invariant system measures system output sensitivity to stationary Gaussian input disturbances of bounded mean anisotropy. Mean anisotropy characterizes the degree of predictability (or colouredness) and spatial non-roundness of the noise. The anisotropic norm falls between the H     

Fixed-interval smoothing of linear discrete systems with multiple time delays

In this correspondence, the problem of fixed-interval smoothing of linear discrete systems with multiple time delays is considered. An algorithm is developed which in certain cases is computationally more efficient than the one obtained through the state augmentation method.     

Walsh function analysis of linear and bilinear discrete time systems

A technique is presented for analysing linear and bilinear discrete systems in terms of Walsh functions. The method replaces the solution of a dynamical difference equation with the solution of an algebraic equation. In the special case of a linear system, a numerically stable recursive technique is derived to solve this algebraic equation. The technique is illustrated with an example.     

Stabilizing static output feedback receding horizon controls for linear discrete time-invariant systems

In this paper, a stabilizing static output feedback receding horizon control (RHC) is proposed for linear discrete time-invariant systems. An inequality condition on the terminal weighting matrices is presented under which the closed-loop stability of static output feedback receding horizon controls is guaranteed. It is shown that the stabilizing static output feedback receding horizon control problem can be represented as a non-linear minimization problem based on linear matrix inequalities (LMIs). An algorithm for solving the presented non-linear minimization problem is proposed. In addition, this result is extended to an arbitrary reference tracking problem that is one of the main features of receding horizon control. Finally, the efficiency of the proposed algorithm is illustrated by numerical examples.     

Iterative learning control for linear discrete time nonminimum phase systems

This paper investigates iterative learning control for linear discrete time nonminimum phase systems. First, iterative learning control with advanced output data is considered for maximum phase systems. Next, the results are extended to nonminimum phase systems. The stability of the inverse mapping from the desired output to the input is proven based on the results for maximum phase systems. The input should be updated with the output which is more advanced than the input by the sum of the relative degree of the system and the number of nonminimum phase zeros. An example is given to indicate the importance of proper advances of output in the input update law.     

Stabilization of linear time varying systems over uncertain channels

In this paper, we study the problem of control of discrete‐time linear time varying systems over uncertain channels. The uncertainty in the channels is modeled as a stochastic random variable. We use exponential mean square stability of the closed‐loop system as a stability criterion. We show that fundamental limitations arise for the mean square exponential stabilization for the closed‐loop system expressed in terms of statistics of channel uncertainty and the positive Lyapunov exponent of the open‐loop uncontrolled system. Our results generalize the existing results known in the case of linear time invariant systems, where Lyapunov exponents are shown to emerge as the generalization of eigenvalues from linear time invariant systems to linear time varying systems. Simulation results are presented to verify the main results of this paper. Copyright © 2012 John Wiley & Sons, Ltd.     

Stabilization bound of discrete two-time-scale systems

In this paper, the exact ε-bound problem in various types of discrete two-time-scale (TTS) system is considered. A set of stability criteria based on the frequency domain representation is derived. Two interesting examples are used to demonstrate the proposed scheme.     

Identification of linear discrete time systems using the instrumental variable method

This paper explores the possibility of using the instrumental variable method to estimate the parameters of linear time-invariant discrete-time systems. The existence of optimal estimates is established, methods for their approximate computation are given, and an on-line identification scheme based on recursive computation is proposed. Experimental results are included.     

Stabilization of linear multivariable systems by output feedback

Absfract-A method is developed for improving the stability of linear multivariable systems using output feedback. The technique, which utilizes a gradient approach, has been mechanized in a digital computer program. Illustrative results are given for a seven-state two-feedback model of the Saturn V booster.     

Model reduction of discrete time systems through linear matrix inequalities*

In this paper, model reduction of discrete time linear systems is revisited. The main objective is to define a convex programming problem expressed in terms of linear matrix inequalities which provides a good suboptimal solution to the model reduction problem. The quality of the proposed suboptimal solution is assessed through comparisons, performed via simulation, with the already classical balanced truncation method. The results lead to the conclusion that the proposed method performs equivalently when the H ₂ norm of the reduction error is considered and significantly better when the H _∞ norm is considered instead.     

Stabilization of switched linear systems

In this note, we study the stabilization problem of systems that switch among a finite set of controllable linear systems with arbitrary switching frequency. For both cases of known and unknown switching functions, feedback laws are designed to achieve exponential stability. For the later case, a method combining on-line adaptive estimation and feedback stabilization is developed in the controller design.     

Stabilization of positive linear systems

We consider stabilization of equilibrium points of positive linear systems which are in the interior of the first orthant. The existence of an interior equilibrium point implies that the system matrix does not possess eigenvalues in the open right half plane. This allows to transform the problem to the stabilization problem of compartmental systems, which is known and for which a solution has been proposed already. We provide necessary and sufficient conditions to solve the stabilization problem by means of affine state feedback. A class of stabilizing feedbacks is given explicitly.     

Quasi-Newton-type optimized iterative learning control for discrete linear time invariant systems

In this paper, a quasi-Newton-type optimized iterative learning control (ILC) algorithm is investigated for a class of discrete linear time-invariant systems. The proposed learning algorithm is to update the learning gain matrix by a quasi-Newton-type matrix instead of the inversion of the plant. By means of the mathematical inductive method, the monotone convergence of the proposed algorithm is analyzed, which shows that the tracking error monotonously converges to zero after a finite number of iterations. Compared with the existing optimized ILC algorithms, due to the superlinear convergence of quasi-Newton method, the proposed learning law operates with a faster convergent rate and is robust to the ill-condition of the system model, and thus owns a wide range of applications. Numerical simulations demonstrate the validity and effectiveness.     

Finite-time event-triggered extended dissipative control for discrete time switched linear systems

This paper considers the problem of finite-time event-triggered extended dissipative control for a class of discrete time switched linear systems. The proposed system is modeled as a discrete time switched linear system with an event-triggered control scheme. Under the event-triggered transmission schemes, we give some sufficient conditions to guarantee the finite-time extended dissipative performance of the closed-loop switched system in terms of linear matrix inequalities. Furthermore, the state feedback controller gains are proposed by solving a set of linear matrix inequalities. Finally, a numerical example is given to show the effectiveness of the proposed methods.