Dynamical analysis of particular class of time-delay control systems

U disertaciji su razmatrani problemi dinamike analize posebnih klasa sistema sa istim vremenskim kašnjenjem. Prošireni su osnovni rezultati na polju ljapunovske stabilnosti linearnih, vremenski diskretnih sistema sa istim vremenskim kašnjenjem. Data je Ljapunov–Krasovski metoda za vremenski diskretne sisteme sa istim vremenskim kašnjenjem. Prezentovani su potrebni i dovoljni uslovi asimptotske stabilnosti, zavisne od isto vremenskog kašnjenja, linearnih, vremenski kontinualnih i diskretnih sistema sa istim vremenskim kašnjenjem. Dati su dovoljni uslovi asimptotske stabilnosti, nezavisne od isto vremenskog kašnjenja, klase linearnih, perturbovanih sistema sa višestrukim vremenskim kašnjenjem. Prezentovani su dovoljni uslovi D–stabilnosti klase linearnih, vremenski diskretnih sistema sa istim vremenskim kašnjenjem. Dati su dovoljni uslovi eksponencijalne stabilnosti vremenski diskretnih sistema sa istim vremenskim kašnjenjem i perturbacijama. Prezentovani su potrebni i dovoljni uslovi kvadratne stabilnosti linearnih, vremenski diskretnih sistema sa istim vremenskim kašnjenjem u stanju i neodreenostima. Potrebni i dovoljni uslovi asimptotske stabilnosti, zavisni od isto vremenskog kašnjenja, velikih, linearnih, vremenski kontinualnih i diskretnih sistema sa istim vremenskim kašnjenjem, su dati. Prouena je stabilnost velikih, intervalnih, vremenski kontinualnih i diskretnih sistema sa istim vremenskim kašnjenjem. Izvedeni su novi dovoljni kriterijumi, zavisni i nezavisni od isto vremenskog kašnjenja, stabilnosti na konanom vremenskom intervalu i atraktivne praktine stabilnosti linearnih, vremenski kontinualnih i diskretnih sistema sa istim vremenskim kašnjenjem, kao i odgovarajui rezultati koji se tiu problema praktine nestabilnosti. Istražen je problema stabilnosti na konanom vremenskom intervalu za klasu linearnih, vremenski diskretnih sistema sa vremenski promenljivim kašnjenjem. Numeriki primeri su dati da demonstriraju primenu prezentovanih metoda.control systems are considered. Some of the basic results in the area of Lyapunov stability of linear, discrete time–delay systems are extended. A Lyapunov–Krasovskii method for discrete time–delay systems is gived. Necessary and sufficient conditions for delay–dependent asymptotic stability of linear, continuous and discrete time–delay systems is offered. Sufficient conditions, independent of delay, for asymptotic stability of a particular class of linear perturbed time–delay systems with multiple delays are gived. New sufficient conditions for the D–stability of a particular class of linear, discrete time–delay systems are established. Sufficient conditions for the exponential stability of discrete time–delay systems with perturbations are gived. Necessary and sufficient conditions for quadratic stability of uncertain linear discrete systems with state delay are presented. New necessary and sufficient conditions for delay–dependent asymptotic stability of a particular class of large–scale, linear, continuous and discrete time–delay systems are established. The stability of continuous and discrete large–scale time–delay interval systems are considered. A new sufficient delay–dependant and delay–independent criteria for the finite time stability and attractive practical stability of linear continuous and discrete time–delay systems has been derived, as well as corresponding results concerning instability problems. Finite–time stability problem has been investigated for a class of linear discrete time–varying delay systems. Numerical examples are given to demonstrate the application of the proposed methods

Linear Matrix Inequality Approach to Robust Emergency Lateral Control of a Highway Vehicle With Time-Varying Uncertainties.

New linear-matrix-inequality (LMI) based methods are developed for the static-output-feedback stabilization and reduced-gain static-output-feedback stabilization of time-invariant systems. Unlike previous methods, the static-output-feedback method is non-iterative in LMI solutions. The methods are extended to design robust static-output-feedback controllers for time-varying systems using a polytopic-systems approach. Examples are given which demonstrate the use of each of the new methods. The specific problem of emergency lateral control of a highway vehicle is then addressed using the new robust static-output-feedback method. A controller is designed which robustly stabilizes the vehicle over the range of highway speeds (15 to 30 m/s) and a range of expected independent changes in front and rear lateral tire stiffness (15 to 30 kN/rad)