Descriptor discretized Lyapunov functional method: analysis and design

This paper presents a design scheme of a minimal order observer-based guaranteed cost controller for uncertain neutral systems, in which some state variables can not be measured. The uncertainties are assumed to be norm-bounded. The initial state is assumed unknown but their mean and covariance are assumed known. A sufficient condition for robust stability analysis and robust stabilization are derived via linear matrix inequalities (LMIs). To show the advantage of the proposed method, a numerical example is given.

Eigenstructure assignment-based robust stability conditions for uncertain systems with multiple time-varying delays

Delay-independent robust stability of uncertain linear systems

The robust stability analysis for discrete large-scale uncertain systems with multiple time delays is addressed in this paper. We establish a method for selecting properly a positive definite matrix Q to derive a very simple upper solution bound of the discrete algebraic Lyapunov equation (DALE). Then, using the Lyapunov equation approach method with this upper bound, several sufficient conditions are presented to guarantee the robust stability of the overall systems. Comparisons between the proposed results with a previous one are also given.

In this paper, the problem of the robust stabilization for a class of uncertain linear dynamical systems with time-varying delay is considered. By making use of an algebraic Riccati equation, we derive some sufficient conditions for robust stability of time-varying delay dynamical systems with unstructured or structured uncertainties. In our approach, the only restriction on the delay functionh(t) is the knowledge of its upper boundh −. Some analytical methods are employed to investigate these stability conditions. Since these conditions are independent of the delay, our results are also applicable to systems with perturbed time delay. Finally, a numerical example is given to illustrate the use of the sufficient conditions developed in this paper.

This correspondence is concerned with an image f(B/sup m/) of a box B/sup m//spl sub/R/sup m/ under a multiaffine transformation f:R/sup m//spl rarr/C. The authors introduce a notion of a principal point of B/sup m/ and prove that the boundary of f(B/sup m/) is covered by images of principal points. The authors exploit this result to provide necessary and sufficient robust stability conditions for polynomials whose coefficients are multiaffine functions of parameters. An application of the general criterion obtained in the correspondence to the particular case of systems with a cascade of first-order uncertain blocks leads to a computationally tractable procedure that verifies stability of the systems. >

In this paper, we consider generalized delay-dependent stability conditions of Takagi-Sugeno fuzzy systems with discrete and distributed time-delays. For fuzzy systems with discrete time-delays, both delay-independent stability conditions and delay-dependent stability conditions have already been obtained. However, no stability condition for fuzzy systems with distributed time-delays has appeared in the literature. This is also true in case of the robust stability for uncertain fuzzy systems with distributed time-delays. With the aid of the stability theorems of linear systems with distributed time-delays, we employ a similar Lyapunov functional for the stability of fuzzy time-delay systems. Then we introduce many free matrices to such a Lyapunov functional, in order to obtain delay-dependent stability conditions. These techniques lead to generalized and less conservative stability conditions. In fact, delay-dependent stability conditions thus obtained are given in linear matrix inequalities(LMIs) and guarantee a wide stability region. We also consider the robust stability of fuzzy time-delay systems with uncertain parameters. Applying the same techniques made on the stability conditions, we obtain delay-dependent sufficient conditions for the robust stability of uncertain fuzzy systems with discrete and distributed time-delays. Moreover, we consider the state feedback stabilization. Based on stability and robust stability conditions, we obtain conditions for the state feedback controller to stabilize the fuzzy time-delay systems. Finally, we take some examples to illustrate our results.

We deal with the robust stabilizability of the class of uncertain linear time-delay systems with Markovian jumping parameters (ULTDSMJP). Under the assumption of complete access to the continuous state and the boundedness of the system's uncertainties, an independent delay sufficient conditions which guarantee the robustness stability of this class of systems are established.

In this paper, we investigate the quadratic stability and quadratic stabilizability of the class of continuous-time linear systems with Markovian jumps and norm-bound uncertainties in the parameters. Under some appropriate assumptions, a necessary and sufficient condition is established for mean-square quadratic stability and mean-square quadratic stabilizability of this class of systems. The quadratic guaranteed cost control problem is also addressed via a LMI optimization problem.

In this paper, we consider robust stability and stabilization of uncertain Takagi-Sugeno fuzzy time-delay systems where uncertainties come into the state and input matrices. Some stability conditions and robust stability conditions for fuzzy time-delay systems have already been obtained in the literature. However, those conditions are rather conservative and do not guarantee the stability of a wide class of fuzzy systems. This is true in case of designing stabilizing controllers for fuzzy time-delay systems and it thus leads to a conservative fuzzy controller design as well. We first consider rather relaxed robust stability conditions of uncertain fuzzy systems. To this end, we introduce an auxiliary system to the original fuzzy time-delay system to obtain generalized delay-dependent stability conditions. Such an auxiliary system has some arbitrary matrices that generalize not only the system representation but also delay-dependent stability conditions. Conditions we obtain here are delay-dependent conditions that depend on the upper bound of time-delay, and are given in terms of linear matrix inequalities (LMIs). Then, we compare our delay-dependent stability conditions with other conditions in the literature, and show that our conditions guarantee the stability of a wider class of systems than others. Next, we consider the robust stabilization problem with memoryless and delayed state feedback controllers. Based on our generalized robust stability conditions, we obtain delay-dependent sufficient conditions for the closed-loop system to be robustly stable, and give a design method of robustly stabilizing controllers. Finally, we give three examples that illustrate our results.

The problem of the robust stability of large-scale dynamical systems including delayed states and parameter perturbations in interconnections is considered. By using algebraic Riccati equations and some analytical methods, some sufficient conditions on linear decentralized state feedback controllers are derived so that the systems remain stable in the presence of delayed states and parameter perturbations. Such conditions give some bounds on the perturbations of interconnections with delayed states and uncertain parameters, and result in a quantitative measures of robustness for large-scale dynamical systems including delayed states and uncertain parameters in interconnections. The results obtained in this paper are applicable not only to large-scale systems with multiple time-varying delays, but also to large-scale systems without exact knowledge of the delays, i.e., large-scale systems with uncertain delays.

An explicit robust stability condition for uncertain time-varying first-order plus dead-time systems

Stabilization of fractional-order singular uncertain systems

We present sufficient conditions for robust relay-delayed semiglobal stabilization of second order systems, which relate the upper bound to an uncertain time delay and the parameters of the plant. We also suggest an algorithm of delayed relay control gain adaptation for semiglobal stabilization, which is based on delayed information about the sign of the controlled variable only. The proposed algorithm suppresses bounded uncertainties in the time delay; that is, being designed for the upper bound of uncertainty in the time delay, the control law ensures semiglobal stabilization independently of any variable time delay obeying the given upper bound.

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.