A new necessary and sufficient condition for static output feedbackstabilizability and comments on “Stabilization via static outputfeedback”

In this paper, a counterexample of the above-mentioned paper by Trofino-Neto et al. (ibid. vol.38 (1993)) is reported. It is pointed out that one of the conditions for a linear system to be stabilizable via static output feedback is not correct. A modified necessary and sufficient condition for this problem is also presented     

Comments on “A new model for control of systems withfriction”

This paper provides a complete stability proof of Theorem 1 of the above-mentioned paper (Canudas-de-Wit et al., 1995) for the tracking and the regulation case. In the paper, the proof presented for Theorem 1 only holds for the regulation case where the LaSalle's invariant principle may be invoked. In the tracking case, the closed-loop system becomes a nonautonomous one, and arguments other than the LaSalle's invariant principle should be used. Here we present these arguments and show that Theorem 1 holds for both cases     

A simple receding horizon control for state delayed systems and its stability criterion

In this paper, a simple receding horizon (or model predictive) control for state delayed systems is presented and its solution is given in a closed form by a reduction method. While the control for a time-delay system is usually complex, the proposed controller is simple to construct and therefore can be simply implemented in real applications. To check the closed-loop stability of the proposed controller, a sufficient condition is provided by linear matrix inequalities. In addition, a numerical algorithm is presented for computing the eigenvalues of systems with distributed time delays, which can be used as a necessary and sufficient condition to check closed-loop stability. It is shown by simulation that this simple control can be a stabilizing control for time-delay systems.     

Parameter convergence in adaptive extremum-seeking control

This paper addresses the problem of parameter convergence in adaptive extremum-seeking control design. An alternate version of the popular persistence of excitation condition is proposed for a class of nonlinear systems with parametric uncertainties. The condition is translated to an asymptotic sufficient richness condition on the reference set-point. Since the desired optimal set-point is not known a priori in this type of problem, the proposed method includes a technique for generating perturbation signal that satisfies this condition in closed-loop. This demonstrates its superiority in terms of parameter convergence. The method guarantees parameter convergence with minimal but sufficient level of perturbation. The effectiveness of the proposed method is illustrated with a simulation example.     

Remarks on minimal solutions of a system of fuzzy relation equations over complete infinitely distributive lattices

In Section 3.6 of Fuzzy relation equations and their applications to knowledge engineering. Kluwer Academic Publishers, Boston (1989), Di Nola et al. presented a procedure to find a minimal solution from a fixed solution of a system of fuzzy relation equations over complete infinitely distributive lattices, and put the question: is the minimal solution found by the procedure unique or not? In this paper, we give a negative answer to the question and make some further remarks. We not only give a necessary and sufficient condition for the uniqueness of such minimal solutions, but also characterize the existence of the least solution and a unique solution of a system of fuzzy relation equations over complete infinitely distributive lattices.     

Design of closed-loop systems with bounded transmission or bounded sensitivity

This paper considers the design, in the frequency domain, of controllers for SISO plants, so that the closed-loop system is asymptotically stable, has a sensitivity function with zeros at given points in Re (s) ?0, and has a transmission or a sensitivity function bounded by a given function. The design requirements are reduced to an interpolation in Re (s) ?0, and a necessary and sufficient condition for its solution is presented. An algorithm is given for the construction of the required controllers.     

Constrained Control of Positive Systems with Delays

This technical note addresses controller design for continuous-time delayed linear systems. The control is under positivity constraint, which means that the resulting closed-loop systems are not only stable, but also positive. Bounded control is also considered, further requiring that the trajectory of the closed-loop system is bounded by a prescribed boundary, if the initial condition is bounded by the same boundary. The contribution lies in three aspects. First, some necessary and sufficient conditions are presented for the existence of controllers satisfying the positivity constraint. Second, a necessary and sufficient condition is established, determining whether the trajectory of a positive system can be bounded by a prescribed boundary, provided that the initial condition is bounded by the same boundary. Third, a sufficient condition is presented for bounded control, and it is shown to be also necessary if asymptotic stability is not required.      

Some necessary and sufficient conditions for eigenstructure assignment

Some necessary and sufficient conditions for closed-loop eigenstructure assignment by output feedback in time-invariant linear multivariable control systems are presented. A simple condition on a square matrix necessary and sufficient for it to be the closed-loop plant matrix of a given system with some output feedback is the basis of the paper. Some known results on entire eigenstructure assignment are deduced from this. The concept of an inner inverse of a matrix is employed to obtain a condition concerning the assignment of an eigenstructure consisting of the eigenvalues and a mixture of left and right eigenvectors.     

Intelligent digital redesign for nonlinear systems using a guaranteed cost control method

In this paper, a novel intelligent digital redesign (IDR) technique using the guaranteed cost control method is proposed for nonlinear systems which can be represented by a Takagi-Sugeno (T-S) fuzzy model. The IDR technique, which is one of the sampled-data fuzzy controller design methods, guarantees not only the stability condition of the sampled-data closed-loop system with the sampleddata fuzzy controller and the state-matching error is presented. By using the concept of the guaranteed cost control method, sufficient conditions are obtained for both minimization of the state-matching error and stabilization of the sampled-data closed-loop system and derived in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to verify the effectiveness of the proposed technique.     

Comments on “A procedure for the positive definiteness offorms of even order”

Hasan and Hasan (IEEE Trans. Automat. Control., Vol.41, p.615-17, 1996) give a necessary and sufficient condition for the positive definiteness of a quadratic programming problem. The purpose of this paper is to point out that the main result in the above-mentioned paper by is erroneous     

Singularity for static-state feedback linearizable bilinear systems

This paper deals with the problem of singularities for a class of static-state feedback linearizable bilinear systems. For this class of nonlinear systems, the decoupling matrix is singular on an algebraic surface (which contains the origin), and this relates the static state feedback linearization to the difficult problem of the completeness of the trajectories of the closed-loop system and/or the boundedness of the feedback laws. In this work, we give a sufficient condition under which all the trajectories of the closed-loop system are complete and the used feedback law is bounded on each of these trajectories     

Existence of (cheap) minimal norm controllers

It is shown that the spectral norm of the closed-loop system matrix is minimized if a special type of minimum variance control is applied. Furthermore, a sufficient condition is derived for the existence of a controller which, with less control effort than this minimum variance controller, obtains the same minimal closed-loop norm.     

受约束的LQ问题与维尼纶絲液温度控制

文中考察受约束的线性二次最优控制问题，给出该问题可解的充分必要条件以及最有综合函数的分析形式。文中还给出最优闭环为全局渐近稳定的充分条件。文中给出的例子说明，最优闭环系统不一定是全局渐近稳定。本文的结果为某工厂的维尼纶丝液温度控制的原理方案提供了合理的、满意的解释。并为实际温控系统的快速性能、抗干扰性能、无超调及无振荡性质等等提供了理论依据。     

不确定时滞系统无记忆鲁棒镇定控制

本文研究了一类状态和控制同时存在滞后的线性时变不确定时滞系统的鲁棒镇定控制问题，针对所有容许的时变未知且有界的不确定性，得到了确保闭环系统二次稳定的充分条件。文中进一步把不确定时滞系统的二次镇定控制器设计问题等价为线性时不变系统的状态反馈标准Ｈ∞控制问题，并由此得到鲁棒镇定控制器综合设计方法。     

Switching Stabilizability for Continuous-Time Uncertain Switched Linear Systems

This paper investigates the switching stabilizability problem for a class of continuous-time switched linear systems with time-variant parametric uncertainties. First, a necessary and sufficient condition for the asymptotic stabilizability of such uncertain switched linear system is derived, under the assumption that the closed-loop switched system does not generate sliding motions. Then, an additional condition is introduced to exclude the possibility of unstable sliding motions. Finally, a necessary and sufficient for the asymptotic stabilizability of such continuous-time uncertain switched linear systems is presented. This result improves upon conditions found in the literature which are either sufficient only or necessary only     

Robust Stabilization for Single-Input Polytopic Nonlinear Systems

This note deals with the stabilization problem of single-input polytopic nonlinear systems. The robust control Lyapunov function approach is used to derive a sufficient condition for the existence of time-invariant, continuous, asymptotically stabilizing state feedback controllers. The obtained sufficient condition is proven also necessary for the existence of stabilizing state feedback controllers such that the closed-loop system has a robust Lyapunov function for all possible uncertainties. In addition, a universal formula for constructing stabilizing controllers when the presented sufficient condition is met is provided. The results are illustrated by a numerical example.     

Finite-time stability of linear time-varying singular systems with impulsive effects

In this paper, we introduce a new concept of finite-time stability of linear time-varying singular systems with impulses at fixed times, and present new results for the above-mentioned class of system in the form of sufficient conditions. A sufficient condition is given in terms of matrix inequalities, which gives the opportunity of fitting the finite-time control problem in the general framework via impulsive control. A numerical example is presented to illustrate the efficiency of the proposed result.     

A new unconditionally stable condition based on singular perturbation analysis

Decentralised configuration with integral control action is the most commonly used control strategy in engineering practice. For decentralised integral control, a desired design target is to achieve closed-loop unconditional stability. Campo and Morari presented steady-state conditions, which can be applied to analyse unconditional stability for most multivariable processes. However, they also showed some processes for which the unconditional stability cannot be determined by only investigating the steady-state gain matrices of the processes. This paper presented an easy to use criterion to determine unconditional stability by using singular perturbation analysis and eigen-value sensitivity analysis. Based on the proposed criterion, the unconditional stability of all the examples presented by Campo and Morari can be easily determined. In the meantime, we proved a conjecture proposed by Campo and Morari (a necessary and sufficient condition for Integral Controllability) for up to all Three-Input and Three-Output systems. For higher dimensional systems, we proposed a new conjecture to simplify the verification of Campo and Morari’s conjecture.