Continuous-time LTI Systems Research Articles

Hybrid Output Feedback Stabilization for LTI Systems With Single Output

This note presents a hybrid control scheme for a class of continuous-time LTI systems that cannot be stabilized by a single static output feedback (SOF) controller. The main idea here is to design multiple SOF gains and proper logic rules that orchestrate switching among these gains so as to achieve the global stability. One challenge, however, is that the switching logic should be in the output feedback form as well. This may seriously restrict the possible choices of switching surfaces, especially when the output is just a scalar. To overcome this difficulty, a multirate sampling control scheme is proposed. Under this framework, a hybrid output feedback stabilizing controller is designed, and sufficient controller synthesis conditions are proposed as linear matrix inequalities based on multiple Lyapunov function theorems. The note concludes with a discussion on possible extensions and future research topics.

Robust H2 filtering for continuous time systems with linear fractional representation

This paper introduces a new approach to H2 robust filtering design for continuous-time LTI systems subject to linear fractional parameter uncertainty representation. The novelty consists on the determination of a performance certificate, in terms of the gap between lower and upper bounds of a minimax programming problem which defines the optimal robust equilibrium cost. The calculations are performed through convex programming methods, applying slack variables, known as multipliers, to handle the fractional dependence of the plant transfer function with respect to the parameter uncertainty. The theory is illustrated by means of a practical application involving an induction motor with uncertain leakage inductance.

Quantizer Design for Interconnected Feedback Control Systems

In this paper, we consider design of interconnected H∞ feedback control systems with quantized signals. We first assume that a decentralized state feedback has been designed for an interconnected continuous-time LTI system so that the closed-loop system is stable and a desired H∞ disturbance attenuation level is achieved, and that the subsystems’ states are quantized before they are passed to the local controller. We propose a local-state-dependent strategy for updating the quantizers’ parameters, so that the overall closed-loop system is asymptotically stable and achieves the same H∞ disturbance attenuation level. We then extend the result to the case of decentralized static output feedback where the measurement outputs are quantized, and propose a local-output-dependent strategy for updating the quantizers’ parameters. Both the pre-designed controllers and the quantizers’ parameters are constructed in a decentralized manner, depending on local information.

Optimal periodic feedback design for continuous-time LTI systems with constrained control structure

This paper aims to design a high-performance controller with any predefined structure for continuous-time LTI systems. The control law employed is the generalized sampled-data hold function (GSHF), which can have any special form, e.g. polynomial, exponential, piecewise constant, etc. The GSHF is first written as a linear combination of a set of basis functions obtained in accordance with its desired form and structure. The objective is to find the coefficients of this linear combination, such that a prespecified linear-quadratic performance index is minimized. A necessary and sufficient condition for the existence of such GSHF is first obtained in the form of matrix inequality, which can be solved by using the existing methods to obtain a set of stabilizing initial values for the coefficients or to conclude the non-existence of such structurally constrained GSHF. An efficient algorithm is then presented to compute the optimal coefficients from their initial values, so that the performance index is minimized. The paper utilizes the latest developments in the area of sum-of-square polynomials. The effectiveness of the proposed method is demonstrated in two numerical examples.

Simultaneous LQ control of a set of LTI systems using constrained generalized sampled-data hold functions

In this paper, sampled-data control of a set of continuous-time LTI systems is considered. It is assumed that a predefined guaranteed continuous-time quadratic cost function, which is, in fact, the sum of the performance indices for all systems, is given. The main objective here is to design a decentralized periodic output feedback controller with a prespecified form, e.g., polynomial, piecewise constant, exponential, etc., which minimizes the above mentioned guaranteed cost function. This problem is first formulated as a set of matrix inequalities, and then by using a well-known technique, it is reformulated as a LMI problem. The set of linear matrix inequalities obtained provides necessary and sufficient conditions for the existence of a decentralized optimal simultaneous stabilizing controller with the prespecified form (rather than a general form). Moreover, an algorithm is presented to solve the resultant LMI problem. Finally, the efficiency of the proposed method is demonstrated in two numerical examples.

Preservation of Lyapunov functions under bilinear mapping

Bilinear mapping preserves quadratic Lyapunov functions between continuous-time and discrete-time LTI systems. This note studies if this property holds for other types of Lyapunov functions specified by vector norms of the system state. Some implications of the obtained results in the common Lyapunov function problems are discussed.

Transfer Functions and Statistical Analysis of FDLCP Systems Described by Higher-order Differential Equations

The paper considers the investigation of finitedimensional linear continuous-time periodic (FDLCP) systems, where the process is described by differential equations of higher than first order, and is influenced by a differentiated input signal. The concept of quasistationary motion mode for such systems is introduced, and closed formulae are derived for calculating statistical characteristics of the quasi-stationary output, when the process is excited by a stationary stochastic signal. Moreover, closed formulae for determining the H2- norm and associated H∞-norms are derived. The methods use a generalization of the parametric transfer matrix (PTM) concept for FDLCP systems of the considered class, and then apply the corresponding classical frequency-domain methods for statistical analysis of continuous-time LTI systems.

DESIGN OF H∞ FEEDBACK CONTROL SYSTEMS WITH QUANTIZED SIGNALS

In this paper, we consider design of H∞ feedback control systems with quantized signals. We first assume that a state feedback has been designed for a continuous-time LTI system so that the closed-loop system is (Hurwitz) stable and a desired H∞ disturbance attenuation level is achieved, and that the states are quantized before they are passed to the controller. We propose a state-dependent strategy for updating the quantizer's parameter, so that the system is asymptotically stable and achieves the same H∞ disturbance attenuation level. We then extend the result to the case of observer-based dynamic output feedback where the measurement outputs are quantized, and propose an output-dependent strategy for updating the quantizer's parameter.

On the synthesis of controllers for continuous time LTI systems that achieve a non-negative impulse response

The problem of controlling the oscillatory response of a system has many practical applications. In this paper, I consider the problem of controlling the sign of the closed loop impulse response for a delay-free LTI system. If the impulse response of a stable system does not change sign, then its step response will neither undershoot nor overshoot. In this paper, I will show that such a synthesis is possible iff the open loop system does not have real, non-minimum phase zeros. In addition, I provide a stable compensator that achieves a stable, non-negative impulse response, if there exists one.

A computational method for simultaneous LQ optimal control design via piecewise constant output feedback

The paper is concerned with simultaneous linear-quadratic (LQ) optimal control design for a set of LTI systems via piecewise constant output feedback. First, the discrete-time simultaneous LQ optimal control design problem is reduced to solving a set of coupled matrix inequalities and an iterative LMI algorithm is presented to compute the feedback gain. Then, simultaneous stabilization and simultaneous LQ optimal control design of a set of LTI continuous-time systems are considered via periodic piecewise constant feedback gain. It is shown that the design of a periodic piecewise constant feedback gain simultaneously minimizing a set of given continuous-time performance indexes can be reduced to that of a constant feedback gain minimizing a set of equivalent discrete-time performance indexes. Explicit formulas for computing the equivalent discrete-time systems and performance indexes are derived. Examples are used to demonstrate the effectiveness of the proposed method.

Time complexity and model complexity of fast identification of continuous-time LTI systems

The problem of fast identification of continuous-time systems is formulated in the metric complexity theory setting. It is shown that the two key steps to achieving fast identification, i.e., optimal input design and optimal model selection, can be carried out independently when the true system belongs to a general a priori set. These two optimization problems can be reduced to standard Gel'fand and Kolmogorov n-width problems in metric complexity theory. It is shown that although arbitrarily accurate identification can be achieved on a small time interval by reducing the noise-signal ratio and designing the input carefully, identification speed is limited by the metric complexity of the a priori uncertainty set when the noise/signal ratio is fixed.