On Robust Stability of Multivariable Interval Control Systems (original) (raw)

New sufficient conditions for robust stability analysis of interval matrices

Systems & Control Letters, 2012

This letter presents new sufficient conditions for robust Hurwitz stability of interval matrices. The proposed conditions are based on two approaches: (i) finding a common Lyapunov matrix for the interval family and (ii) converting the robust stability problem into a robust non-singularity problem using Kronecker operations. The main contribution of the letter is to derive accurate and computationally simple optimal estimates of the robustness margin and spectral bound of general interval matrices. The evaluation of the condition relies on the solutions of linear matrix inequalities (LMIs) and eigenvalue problems, both of which are solved very efficiently. The improvements gained by using the proposed conditions are demonstrated through application to previous examples in the literature.

Parametric Stability Margin for Multilinear Interval Control Systems

1993 American Control Conference, 1993

Recently, a necessary and sufficient conditionto determine the robust stability of a multilinearinterval controlsystem has been reported in [i,2] as an extension of the weN-known Box theorem [3]which deals with the linearaffinecase. This paper introduces a simple but computationally efficient algorithm,based on the above result,to check the robust stability of such systems. The method is also extended to find the parametric stability margin of such a system.

Sufficient conditions for the stability of interval matrices

International Journal of Control, 1993

In this paper, the global asymptotic stability of interval systems with multiple unknown time-varying delays is considered. Some criteria are derived to guarantee the global asymptotic stability of such systems. A numerical example is provided to illustrate the use of our main results.

Stability Analysis of the Interval Systems Based on Linear Matrix Inequalities

Springer Nature, 2019

Positive definiteness and Hurwitz stability of the interval systems are discussed. A linear matrix inequality representation is introduced to simplify the analysis of the interval system. First, it is shown that the interval matrix can be stable if it has 2 conditions. Afterward, they converted to linear matrix inequalities for simplifying the conditions solution. A Lyapunov function is introduced to prove the new representation based on linear matrix inequalities.

Robust control of interval systems

Robust Control

In this paper we consider a feedback interconnection of two linear time invariant systems, one of which is fixed and the other is uncertain with the uncertainty being a box in the space of coefficients of the numerator and denominator polynomials. This kind of system arises in robust control analysis and design problems. We give several results for the Nyquist plots and stability margins of such families of systems based oil the extremal segments of rational functions introduced by Chapellat and Bhattadaaryya [1]. These CB segments play a fundamental characterizing role in many control design problems.

Robust Design of State-Derivative Feedback Controllers for Linear Time-Invariant Interval Systems

Anais do 14º Simpósio Brasileiro de Automação Inteligente

This paper presents a technique for state-derivative feedback control design applied to singleinput and multiple-input linear time-invariant uncertain systems whose parameters belong to closed intervals. It is proposed an interval extension of a direct design method for state-derivative feedback controllers by state feedback design. It is considered a computational optimization-based procedure, formulated as an interval goal programming problem, equivalent to the interval Ackermann's equation for the robust eigenvalue placement problem. The design objective is the minimization of the overall deviation from the spectral set of the interval closed-loop polynomial related to the limits of performance specifications for the transient response.

Stability and Set-Invariance Testing for Interval Systems

2008

Many works dealing with the stability analysis of interval systems developed criteria based on matrices that majorize (in a certain sense) the interval matrices describing the system dynamics. Besides this already classical employment, we prove that the majorant matrices also contain valuable information for the study of the exponentially decreasing sets, invariant with respect to the trajectories of the interval systems. The interval systems are considered with both discrete-and continuous-time dynamics. The invariant sets are characterized by arbitrary shapes, defined in terms of Hőlder vector p-norms, 1 p ≤ ≤ ∞ . Our results cover two types of interval systems, namely described by interval matrices of general form and by some particular classes of interval matrices. For the general case, we formulate necessary and sufficient conditions, when the shape of the invariant sets is defined by the norms 1, p = ∞ , and sufficient conditions, when the shape is defined by the norms 1 p < <∞ . For the particular cases, we provide necessary and sufficient conditions for all norms 1 p ≤ ≤∞ .

Componentwise Stabilization of Interval Systems

Proceedings of the 17th IFAC World Congress, 2008, 2008

The componentwise stability of a linear system is a special type of asymptotic stability induced by the existence of exponentially decreasing rectangular sets that are invariant with respect to the free response. An interval system ( )