Analysis and controller design of discrete-time linear systems with state saturation

This paper deals with the question of the existence of weak and strong common
\nquadratic Lyapunov functions (CQLFs) for stable discrete-time linear timeinvariant
\n(LTI) systems. The main result of the paper provides a simple characterisation
\nof pairs of such systems for which a weak CQLF of a given form exists
\nbut for which no strong CQLF exists. An application of this result to second
\norder discrete-time LTI systems is presented.

This paper reviews robust feedback control applications in power system. Robust control concept in power system control area evolves by the way of uncertainty modeling. Uncertainties can be caused by variation of loading, load parameters, network topology and machine parameters. One direct way to take into consideration of uncertainties is to enumerate various system operating conditions and use a set of linear time invariant systems to model the power systems. Enumeration method is used in robust control signal selection and robust controller design. Another way is to model uncertainties as structured or unstructured uncertainties. Controllers are designed based on nominal system condition to tolerate uncertainty as much as possible. The controller synthesis problem is solved by either Algebraic Ricatti Equation (ARE) or Linear Matrix Inequality (LMI). LMI is shown to be more flexible in controller design since it provides a way to specify system dynamic performance. Most recently, linear parameter varying (LPV) concept expands the use of enumeration method to express a set of linear time invariant (LTI) systems with state space dependent on linear parameters. LPV based control methods extend gain scheduling to design linear control for each operating conditions and overall a nonlinear controller for the varying parameter system.

In this paper, a decentralized overlapping static output feedback law is proposed to control a linear time-invariant (LTI) interconnected system. It is assumed that an overlapping information flow structure is given which determines which output measurements are available for any local control agent. Uncertain transmission delay is also considered in communication links among different subsystems. Each subsystem is assumed to be subject to input disturbances with finite energy. A necessary condition for the existence of a stabilizing overlapping controller is obtained which is easy to check. Furthermore, a linear matrix inequality (LMI) based design methodology is proposed to achieve internal stability and H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> disturbance attenuation. Simulations are presented to demonstrate the efficacy of the developed results.

This paper is concerned with the decentralized H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> controller synthesis problem for discrete-time linear time-invariant (LTI) systems. In spite of intensive research efforts over the last several decades, this problem is believed to be non-convex and still outstanding in general. Therefore most existing approaches resort to heuristic optimization algorithms that do not allow us to draw any definite conclusion on the quality of the designed controllers. To get around this difficult situation, in this paper, we propose convex optimization procedures for computing lower bounds of the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance that is achievable via decentralized LTI controllers of any order. In particular, we show that sharpened lower bounds can be obtained by making good use of structures of the LTI plant typically observed in the decentralized control setting. We illustrate via numerical examples that these lower bounds are indeed useful to ensure the good quality of decentralized controllers designed by a heuristic optimization.

This paper studies the problem of reliable Hinfin state feedback controller design for linear continuous-time systems. Actuator partial failures and actuator lock-in-place failures are simultaneously considered, and the signals in the case of certain actuators being locked in place are treated as zero-frequency disturbances, which gives an exact description for the lock-in- place failures. Based on the generalized KYP lemma in finite frequency domain, the controller design is developed in the framework of linear matrix inequality (LMI) approach, which can guarantee the asymptotic stability and Hinfin performances of the resulting closed-loop systems when all control components are operational as well as when some actuators fail. Finally, the design procedure and the effectiveness of the proposed method in comparison with the entire frequency approach by using bounded real lemma are illustrated via a numerical example of flight tracking control of an F-16 aircraft.

Parameter Estimation in Input Matrix Under Gain Constraints in Specified Frequency Ranges

The stability analysis and controller design of discrete linear systems with time-varying delay are addressed. Firstly, the uniformly asymptotical stability criterion with adjustable parameter is derived by Lyapunov-Razumikhin approach. Then, the stabilization approaches for linear systems with time delay by state feedback and observer based-on state feedback are also presented. Sufficient conditions for the existence of state feedback gain and the observer gain are derived through the numerical solution of a set of obtained linear matrix inequalities. Compared with methods in the references, the dynamic performance of systems, such as the overshoot and the convergence rate of the response, can be adjusted by changing the adjustable parameter. Lastly, an illustrative example is given to show the effectiveness of the proposed.

This paper addresses the decentralized control problem of a class of discrete-time linear time-invariant (LTI) systems composed of two interconnected subsystems. By means of the well-known projection theorem, a suf.cient stability condition of such systems is established, which is less conservative than the existing results. This condition is then extended to the case where the systems involve delays. All the conditions can be veri.ed by a combination of linear matrix inequalities (LMI) toolbox and optimal search algorithm of Matlab. Numerical example is provided to illustrate the effectiveness and advantages of the obtained results.

Discrete-Time H∞ Preview Feedforward Controller Using Uncertain Prior External Input Information via GKYP Lemma

We present a couple of data-based methods to analyze the state controllability and state observability of discrete-time Linear time-Invariant (LTI) systems with time-delays, which have unknown parameter matrices. They first augment the system into a high dimensional LTI model, then apply the measured state and output data to directly build the controllability and observability matrices respectively of this high dimensional model, whose ranks are used as the criteria of the corresponding properties of the system before augmentation. These data-based methods have low computational load and calculation complexity.

For continuous-time linear time-invariant (LTI) systems with polytopic uncertainties, we develop a robust sampled-data state-feedback control design scheme in terms of linear matrix inequalities (LMIs). Truncated power series expansions are used to approximate a discretized model of the original continuous-time system. The system matrices obtained by using the power series approximations are then expressed as homogeneous polynomial parameter-dependent (HPPD) matrices of finite degrees, and conditions for designing the controller are formulated as a HPPD matrix inequality, which can be solved by means of a recent LMI relaxation technique to test the positivity of HPPD matrices with variables in the simplex. To take care of the errors induced by the remainder terms of the truncated power series, the terms are considered as norm bounded uncertainties and then incorporated into the proposed LMI conditions. Finally, examples are used to illustrate the approach.

Hybrid control for non-overshooting step responses of linear systems

Robust stability analysis of polytopic linear time-invariant (LTI) systems is a basic problem in engineering. This paper analyzes the complexity of three fundamental methods used to address this problem, all of them providing a sufficient and necessary condition (with finite and known sizes) for robust stability. The first method is based on the use of a polynomially parameter-dependent Lyapunov function. The second method is a simplified version of the Routh-Hurwitz stability criterion. Lastly, the third method is based on eigenvalue combinations. It is explained that the robust stability conditions provided by these three methods require to establish positive definiteness of symmetric matrix forms (SMFs) over the simplex. Also, it is explained that a sufficient condition for the latter problem can be given in terms of a linear matrix inequality (LMI) feasibility test. Hence, the complexity of the three methods is analyzed and compared by deriving the number of scalar variables in the LMI feasibility tests. A numerical example is also presented to investigate the computational time of these tests.

Frequency-domain stability conditions for asynchronously sampled decentralized LTI systems

This study investigates characteristic root equivalency relations between commensurate order and integer order Linear Time Invariant (LTI) systems. Author introduces some useful properties of a special class of commensurate order systems, which is called characteristic root equivalency class of LTI systems. These properties present potential to facilitate design and analysis efforts of this class of commensurate order systems. In this sense, straightforward stability checking procedures and design approaches for commensurate order root equivalent systems of the first and second order LTI systems are demonstrated. Findings of the study are validated by illustrative examples.