Robust Filtering In Time-Delay Switched Systems

As an important class of hybrid systems, switched systems can mimic the practical plants efficiently rather than general linear systems, such as power systems, wireless sensor networks, which are attracted much attention. As one of the hot topics in control theory, control and estimation problems to switched systems have been achieved lots of results. However, time delay and nonlinearity are unavoidable which may lead to degradation of system performance. On the other hand, the modeling uncertainties and external distur-bances with unknown statistical characteristics also affect the systems. The paper takes the multi-factors into accounts, and investigates the robust estimation problem of switched systems.After the essential differences between switched systems and general systems are an-alyzed, a filter is provided for the system with restricted switching scheme based on Lya-punov stability and average dwell time. The link between dwell time and estimation perfor-mance is explored. The following problems are considered:robust multi-objective filtering problems for uncertain systems, H? filtering problems for nonlinear switched systems with neutral delay type as well as distributed delay type, the generalized H2 non-fragile filter-ing problem for discrete-time switched systems, and the strictly (Q,S,R)-? dissipative filtering problem for singular switched systems.The problem of multi-objective robust filtering is investigated for continuous-time sys-tems with poly topic type parameter uncertainties. For a class of nominal uncertain system, a new necessary and sufficient condition is derived based on bounded real lemma, which guarantees the filtering error system to be robustly a-stable and achieves a prescribed gen-eralized performance. For another uncertain system with time-varying delays, by choosing appropriate parameter-dependent Lyapunov-Krasovskii functional and adopting free weight matrices approach, the parameter-dependent filter is designed to ensure the filtering error system being generalized H2/? stable. In the process of linearization, we decouple the fil- tering gain matrices from the Lyapunov matrices by introducing some additional matrices, finally the condition for the existence of parameter-dependent filter is presented in terms of a set of LMIs that simplify the design of the filter.The exponential H? filtering problem is investigated for a class of delayed nonlinear switched systems of neutral-type. The nonlinearity is assumed to satisfied the Lipschitz condition. With the aid of average dwell time method, we provide a delay-dependent suf-ficient condition, under which the designed filter satisfies H? noise attenuation and expo-nential stability. The condition depends on discrete delay as well as neutral delay which reduces the conservatism of the results. Since some realistic factors including delays, dis-turbance and topology changes are generally exist in biological neural nets, the well-known leaky integrate-and-fire model is modified as a switched neural network so that function of a single neuron is identified via the H|infty filtering instead of biological experimen-tal methods. Two examples are given to show the effectiveness of the proposed design algorithm.We focus on a class of mixed delayed nonlinear switched systems with integral delay term, and investigate the asynchronous H? filtering problem since the switching signals delayed. A more generalized sector nonlinearity is considered. Based on Lyapunov sta-bility theory, we analyze both the exponential stability of system on matched period and mismatched period respectively, and the H? performance with the external disturbance. An example of filtering of recursive neural networks is verified the effectiveness of the proposed method.The robust non-fragile generalized H2 filtering is discussed for a class of discrete-time delayed nonlinear switched systems. On account of the round-off errors in numerical com-putation or programming errors in the process of filter implementation, uncertainties are aroused, so that the design of a less sensitive filter is concerned. A stochastic variable is introduced to depict random occurrence of the filter gain variation, and the uncertainties of the filter is norm bounded. By taking advantages of a modified reciprocally convex com-bination approach, a sufficient condition is obtained that ensures the filtering error system being exponentially stable in mean square sense and achieves a prescribed generalized H2 performance level. A numerical example is illustrated the validity of the proposed design method.The strictly (Q,S,R)-?-dissipative filtering problem is studied for discrete-time singular switched systems with time-varying delays. By extending a delay partitioning idea into the mode-dependent Lyapunov functional and adopting average dwell time method, a less conservative criterion is established to warrants the exponential admissibility and dissipativity of the filtering error system. The strictly (Q, S, R)-?-dissipative filter can be obtained from the solution of convex optimaization problems.