In this paper the necessary and sufficient conditions are given for the solution of a system of parameter varying linear inequalities of the form ( ) ( ) t t ≥ A x b for all t T ∈ , where T is an arbitrary set, x is the unknown vector, ( ) t A is a known triangular Toeplitz matrix and ( ) t b is a known vector. For every t T ∈ the corresponding inequality defines a polyhedron, in which the solu...

In this paper the necessary and sufficient conditions are given for the solution of a system of parameter varying linear inequalities of the form A (t)x ≥ b (t) for all t ∈ T , where T is an arbitrary set, x is the unknown vector, A (t) is a known triangular Toeplitz matrix and b (t) is a known vector. For every t ∈ T the corresponding inequality defines a polyhedron, in which the solution shou...

This study introduces the fuzzy Lyapunov function to the fuzzy PID control systems, modified fuzzy systems, with an optimized robust tracking performance. We propose a compound search strategy called conditional linear matrix inequality (CLMI) approach which was composed of the proposed improved random optimal algorithm (IROA) concatenated with the simplex method to solve the linear matrix ineq...

This paper considers interval time-varying delay systems. The time-delay interval is divided into several zones and the systems switch among the different zones. Based on LyapunovKrasovskii functional methods and linear matrix inequality (LMI) techniques, Exponential stability is exploited for every time-delay zone. The global stability of the switched system is guaranteed if some minimum avera...

This paper deals with several challenging problems of robust filtering for two-dimensional (2-D) systems. First of all, new linear matrix inequality (LMI) characterizations for the and 2 norms of 2-D systems are introduced and thoroughly established. Based on these preparatory results, convex (LMI) characterizations for robust , 2, and robust mixed 2 filtering are derived. The efficiency and vi...

This technical note investigates the problem of checking robust -stability of a polytope of polynomial matrices. Finsler’s projection lemma is taken to derive a new sufficient condition in terms of a linear matrix inequality (LMI) feasibility problem. The basic idea behind this condition is to lift the existing stability condition into the one of larger space by means of Finsler’s lemma and, ba...

Abs t rad -Th i s paper presents all controllers for the general ~'® control problem (with no assumptions on the plant matrices). Necessary and sufficient conditions for the existence of an ~® controller of any order are given in terms of three Linear Matrix Inequalities (LMIs). Our existence conditions are equivalent to Scherer's results, but with a more elementary derivation. Furthermore, we ...

This paper investigates the robust stability of linear neutral time-varying delay systems with non-linear perturbations. The uncertainties under consideration are nonlinear time-varying parameter perturbations and norm-bounded uncertainties, respectively. Using new Lyapunov-Krasovskii functional and integral inequality matrices, less conservative delay-dependent robust stability conditions for ...

This paper provides an exact linear matrix inequality (LMI) condition for robust asymptotic stability of uncertain systems depending polynomially on a scalar parameter in both continuous-time and discrete-time cases. Specifically, this condition exploits sum of squares (SOS) techniques and is based on the construction of polynomials of known degree that detect the presence of eigenvalues on the...