Quadratic stabilization of continuous time systems with state-delayand norm-bounded time-varying uncertainties

This paper develops a method for designing a feedback control law to stabilize a class of uncertain linear systems. The class of systems under consideration is described by a continuous-time model with variable-state delay and depends on time-varying unknown-but-bounded uncertain parameters. It is shown that the construction of the stabilizing controller involves solving a certain algebraic Riccati equation. Several previous results are derived as interesting special cases. Finally, a simulation example is presented to illustrate the analytical developments     

Quadratic stability and stabilization of linear systems withFrobenius norm-bounded uncertainties

In this paper, a quadratic stability condition and a quadratic stabilizer are proposed for linear systems with Frobenius norm-bounded uncertainties. The necessary and sufficient condition for the quadratic stability of the uncertain system is given by a Riccati inequality. The proposed state feedback quadratic stabilizer can be obtained by solving a Riccati equation     

Comments on "Quadratic stability and stabilization of dynamic interval systems"

In the above paper, it was claimed that the necessary and sufficient conditions for the quadratic stability and stabilization of dynamic interval systems are given in terms of linear matrix inequalities (LMIs). In this note, numerical examples are presented to show that the necessity of the conditions given in does not hold.     

Robust stabilization of linear systems with norm-bounded time-varying uncertainty

In this paper, robust stabilization of a class of linear systems with norm-bounded time-varying uncertainties is considered. It is shown that for this class of uncertain systems quadratic stabilizability via linear control is equivalent to the existence of a positive definite symmetric matrix solution to a (parameter-dependent) Riccati equation. Also, a construction for the stabilizing feedback law is given in terms of the solution to the Riccati equation.     

Comments on “Explicit asymmetric bounds for robust stabilityof continuous and discrete-time systems”

Referring to the original paper by Gao and Antsaklis (ibid., vol. 38, p. 332-5, 1993), the authors state that Theorem 2 is incorrectly stated. A correct version of the theorem is provided     

Comments on “Identification for systems with boundednoise”

In the above-mentioned paper by Tan et al. (1997), the authors claimed that the estimation error of their identification algorithm is non-increasing. We show in this note that this statement is misleading, and point out the mistake made in their derivation of the statement. We further show that the worst-case estimation error of their algorithm is, however, non-increasing     

Comments on “D-stability of continuous time-delay systemssubjected to a class of highly structured perturbations”

In this paper, we wish to point out that the proof of the main results in the above-mentioned paper by Lee (ibid. vol.40 (1995)) is incorrect. Furthermore, we verify that there exists no continuous time-delay system guaranteeing the D(α, r)-stability     

Comments on “Further studies on LMI-based relaxed stabilization conditions for nonlinear systems in Takagi-Sugeno’s form”

This paper points out that Corollary 1 is equivalent to Proposition 1 in [Ding, B. C., Sun, H. X., & Yang, P. (2006). Further studies on LMI-based relaxed stabilization conditions for nonlinear systems in Takagi-Sugeno’s form. Automatica, 42(3), 503-508].     

Comments on “Hierarchical cubic networks”

Ghose and Desai (1995) introduced a new interconnection for large-scale distributed memory multiprocessors called the Hierarchical Cubic Network (HCN). The HCN is topologically superior to a comparable hypercube. They also proposed optimal routing algorithms for the HCN and obtained its diameter, which is about three-fourths the diameter of a comparable hypercube. However, their routing algorithm is not distance-optimal. In this paper, we propose an optimal routing algorithm for the HCN and show that HCN has about two-thirds the diameter of a comparable hypercube     

Comments on “Robust adaptive regulation with minimal priorknowledge”

The author comments on the paper by F. Giri et al. (see ibid., vol.37, no.3, p.305-15, 1992). The author argues that there is a circularity in the argument of the paper and that therefore, the correctness of the results of the paper is ambiguous     

Comments on “Robust stability of linear systems with delayedperturbations”

The paper points out that in Kim (1996), the concavity of the function is falsely defined, so the proof in the appendix in the paper is wrong. A corrected version of the proof is provided     

Comments on “The Model Checker SPIN”

The paper by G.J. Holzmann (see ibid., vol.23, no.5, p.279-95, 1997) describes how to apply SPIN to the verification of a synchronization algorithm (L.M. Ruane, 1990) in process scheduling of an operating system. We report an error in the verification model presented by G.J. Holzmann and present a revised model with verification result. Our result explains the reason why SPIN found the race condition in the synchronization algorithm. We also show that the suggested fix by G.J. Holzmann is incorrect     

Comments on “Optimally switched linear systems”

The technical note titled “Optimally switched linear systems” by the authors T. Das and R. Mukherjee addresses the problem of optimal switching for switched systems. The proof of the theorem in the paper is incorrect and point out an important theoretical point which explains why the optimal switched solution does not exist whenever there exists a singular one to a relaxed problem. This point has also important consequences concerning numerical difficulties encountered in solving such problems and are also discussed.     

Local stabilization for linear discrete-time systems with bounded controls and norm-bounded time-varying uncertainty

The problem of the local stabilization of linear discrete-time systems subject to bounded controls and suffering from uncertainty of the norm-bounded time-varying type is addressed. From the solution of a certain discrete Riccati equation, a control gain and a set of safe initial conditions are obtained. The asymptotic stability of the saturated closed-loop system is then locally guaranteed for all admissible uncertainties. It is also shown how the control problem can be translated into L.M.I. conditions. The connections between local stability results and disturbance rejection problem are investigated. In the presence of control saturation, it is thus shown that it is possible to reject a certain class of perturbations. Finally, a discretized model of the inverted pendulum allows us to illustrate the results. © 1998 John Wiley & Sons, Ltd.     

Comments on “Distinguishability quantification of fuzzy sets”

This paper presents some comments on the above paper regarding the manipulation of Gaussian fuzzy sets and provides two useful generalized formulas for both of similarity and similarity/possibility relationships of Gaussian fuzzy sets with different widths.     

Quadratic stabilization of sampled-data systems with quantization

A design method of memoryless quantizers in sampled-data systems is proposed. The design objective is quadratic stability in the continuous-time domain, and thus the decay rate between sampling times is guaranteed. Our general treatment enables us to look for quantizers efficient in terms of data rate.     

Comments on “A modification and the Tustinapproximation” with a concluding proposition

In the original paper (K.B. Janiszowski, ibid., vol. 38, no. 8, p. 1313-16, 1993) there is presented a modification of the Tustin approximation. The author argues that the justification of this modification, by means of three examples, is not convincing, because the choice of the examples is questionable and some calculations are not sufficiently accurate. It is shown that some good properties of the proposed modification can be justified by using the Tustin approximation of a continuous-time (CT) model for the discrete-time (DT) system. It is stressed that the proposed modification has only a limited value, since from application point of view the use of CT models is more reasonable. As the conclusion the DT controller design procedure by using CT methods is proposed     

Comments on “Zeros of discretized continuous systemsexpressed in the Euler operator-an asymptotic analysis” [andreply]

In the original paper by Tesfaye and Tomizuka (ibid., vol.40, p.743-7, 1995), an asymptotic analysis was used to address the zero structure of discretized continuous-time systems expressed in the Euler (or forward difference) operator. The method was developed for application to multivariable control systems. The authors state that the analysis is flawed, so that a theorem is true as stated only when the continuous time relative degree is equal to two. They indicate how the analysis may be rectified. Tesfaye and Tomizuka acknowledge the error and the correctness of the result in this paper     

A comment on “Decentralized stabilization of large scaleinterconnected systems with delays”

Hu claims new results in the above mentioned paper (ibid. vol.39, no.1, p.180-2 (1994)) regarding decentralized stabilization of large scale interconnected systems with delays. This note shows that the results presented in Theorems 1 and 2 and Corollaries 1 and 2 apply only to a very restrictive class of systems for which the number of inputs and outputs is equal to the number of states. An alternative stability condition is provided, which improves the existing one